# Chapter 21: Electromagnetic Introduction And Faraday's Law

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• 1.

### All of the following are units of magnetic flux except

• A.

T*m^2.

• B.

T/V*m.

• C.

Weber.

• D.

V*s.

B. T/V*m.
Explanation
The correct answer is T/V*m. Magnetic flux is a measure of the quantity of magnetic field passing through a given area. The units of magnetic flux are typically measured in webers (Wb) or volt-seconds (V*s). T*m^2 represents the unit for magnetic moment, which is a different concept. Therefore, T/V*m is not a valid unit for magnetic flux.

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• 2.

### Faraday's law of induction states that the emf induced in a loop of wire is proportional to

• A.

The magnetic flux.

• B.

The magnetic flux density times the loop's area.

• C.

The time variation of the magnetic flux.

• D.

Current divided by time.

C. The time variation of the magnetic flux.
Explanation
Faraday's law of induction states that the electromotive force (emf) induced in a loop of wire is proportional to the time variation of the magnetic flux passing through the loop. This means that the magnitude of the induced emf is directly related to how quickly the magnetic flux changes over time. The other options, such as the magnetic flux, the magnetic flux density times the loop's area, and current divided by time, are not correct as they do not accurately describe Faraday's law of induction.

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• 3.

### Doubling the number of loops of wire in a coil produces what kind of change on the induced emf, assuming all other factors remain constant?

• A.

The induced emf is 4 times as much.

• B.

The induced emf is twice times as much.

• C.

The induced emf is half as much.

• D.

There is no change in the induced emf.

B. The induced emf is twice times as much.
Explanation
When the number of loops of wire in a coil is doubled, the induced emf (electromotive force) also doubles. This is because the induced emf is directly proportional to the number of loops in the coil. Therefore, if the number of loops is doubled, the induced emf will also double.

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• 4.

### Doubling the strength of the magnetic field through a loop of wire produces what kind of change on the induced emf, assuming all other factors remain constant?

• A.

The induced emf is 4 times as much.

• B.

The induced emf is twice as much.

• C.

The induced emf is half as much.

• D.

There is no change in the induced emf.

B. The induced emf is twice as much.
Explanation
When the strength of the magnetic field through a loop of wire is doubled, the induced emf also doubles. This is because the induced emf is directly proportional to the rate of change of magnetic flux, and doubling the magnetic field strength doubles the rate of change of magnetic flux. Therefore, the induced emf is twice as much.

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• 5.

### Doubling the diameter of a loop of wire produces what kind of change on the induced emf, assuming all other factors remain constant?

• A.

The induced emf is 4 times as much.

• B.

The induced emf is twice times as much.

• C.

The induced emf is half as much.

• D.

There is no change in the induced emf.

A. The induced emf is 4 times as much.
Explanation
When the diameter of a loop of wire is doubled, the area of the loop increases by a factor of 4 (since area is proportional to the square of the diameter). According to Faraday's law of electromagnetic induction, the induced emf is directly proportional to the rate of change of magnetic flux through the loop. Since the area of the loop has increased by a factor of 4, the magnetic flux through the loop will also increase by a factor of 4. Therefore, the induced emf will be 4 times as much.

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• 6.

### As a coil is removed from a magnetic field an emf is induced in the coil causing a current to flow within the coil. This current interacts with the magnetic field producing a force which

• A.

Acts at right angles to the coil's motion.

• B.

Acts in the direction of the coil's motion.

• C.

Causes the coil to tend to flip over.

• D.

Acts in the direction opposite to the coil's motion.

D. Acts in the direction opposite to the coil's motion.
Explanation
As a coil is removed from a magnetic field, the change in magnetic flux through the coil induces an electromotive force (emf) in the coil according to Faraday's law of electromagnetic induction. This emf causes a current to flow within the coil. According to the right-hand rule, the direction of the induced current creates a magnetic field that opposes the change in the original magnetic field. This means that the magnetic force experienced by the coil acts in the direction opposite to the coil's motion, in order to try to maintain the original magnetic field.

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• 7.

### According to Lenz's law, the direction of an induced current in a conductor will be that which tends to produce which of the following effects?

• A.

Enhance the effect which produces it

• B.

Produce a greater heating effect

• C.

Produce the greatest voltage

• D.

Oppose the effect which produces it

D. Oppose the effect which produces it
Explanation
According to Lenz's law, the direction of an induced current in a conductor will always be such that it opposes the change or effect that produces it. This is because the induced current creates a magnetic field that opposes the change in the magnetic field that caused the current to be induced in the first place. This is a fundamental principle of electromagnetic induction and is consistent with the law of conservation of energy.

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• 8.

### A circular coil lies flat on a horizontal table. A bar magnet is held above its center with its north pole pointing down. The stationary magnet induces (when viewed from above)

• A.

No current in the coil.

• B.

A clockwise current in the coil.

• C.

A counterclockwise current in the coil.

• D.

A current whose direction cannot be determined from the information given.

A. No current in the coil.
Explanation
When a bar magnet is held above the center of a circular coil, the magnetic field lines from the magnet pass through the coil. However, since the magnet's north pole is pointing down and the coil is lying flat on the table, the magnetic field lines passing through the coil are parallel to the plane of the coil. In this configuration, there is no change in the magnetic flux passing through the coil, and therefore no current is induced in the coil according to Faraday's law of electromagnetic induction. Hence, the correct answer is no current in the coil.

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• 9.

### A circular coil lies flat on a horizontal table. A bar magnet is held above its center with its north pole pointing down, and released. As it approaches the coil, the falling magnet induces (when viewed from above)

• A.

No current in the coil.

• B.

A clockwise current in the coil.

• C.

A counterclockwise current in the coil.

• D.

A current whose direction cannot be determined from the information provided.

C. A counterclockwise current in the coil.
Explanation
As the north pole of the bar magnet approaches the coil, it induces a counterclockwise current in the coil. This is due to Faraday's law of electromagnetic induction, which states that a changing magnetic field induces an electromotive force (EMF) in a conductor. In this case, the changing magnetic field caused by the approaching magnet induces a counterclockwise current in the coil.

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• 10.

### A coil lies flat on a table top in a region where the magnetic field vector points straight up. The magnetic field vanishes suddenly. When viewed from above, what is the sense of the induced current in this coil as the field fades?

• A.

The induced current flows counterclockwise.

• B.

The induced current flows clockwise.

• C.

There is no induced current in this coil.

• D.

The current flows clockwise initially, and then it flows counterclockwise before stopping.

A. The induced current flows counterclockwise.
Explanation
When the magnetic field suddenly vanishes, according to Faraday's law of electromagnetic induction, an induced current is generated in the coil. The direction of the induced current is determined by Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic field. In this case, since the magnetic field is pointing straight up and suddenly disappears, the induced current will flow counterclockwise to create a magnetic field that opposes the disappearance of the original magnetic field. Therefore, the correct answer is that the induced current flows counterclockwise.

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• 11.

### A coil lies flat on a level table top in a region where the magnetic field vector points straight up. The magnetic field suddenly grows stronger. When viewed from above, what is the direction of the induced current in this coil as the field increases?

• A.

Counterclockwise

• B.

Clockwise

• C.

Clockwise initially, then counterclockwise before stopping

• D.

There is no induced current in this coil.

B. Clockwise
Explanation
As the magnetic field vector points straight up and suddenly grows stronger, according to Faraday's law of electromagnetic induction, an induced current will be generated in the coil. The induced current will flow in a direction that opposes the change in magnetic field. Since the magnetic field is increasing in strength, the induced current will flow in a direction that creates a magnetic field opposing the upward direction. Using the right-hand rule, when viewed from above, the induced current will flow in a clockwise direction.

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• 12.

### A coil lies flat on a horizontal table top in a region where the magnetic field points straight down. The magnetic field disappears suddenly. When viewed from above, what is the direction of the induced current in this coil as the field disappears?

• A.

Counterclockwise

• B.

Clockwise

• C.

Clockwise initially, then counterclockwise before stopping

• D.

There is no induced current in this coil.

B. Clockwise
Explanation
When the magnetic field disappears suddenly, Faraday's law of electromagnetic induction states that an induced current will be generated in the coil. According to Lenz's law, the direction of the induced current will be such that it opposes the change that caused it. In this case, the sudden disappearance of the downward magnetic field would create a change that induces a current in the coil that flows in the same direction as the original field. Therefore, the direction of the induced current in the coil as the field disappears would be clockwise.

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• 13.

### A long straight wire lies on a horizontal table and carries an ever-increasing current northward. Two coils of wire lie flat on the table, one on either side of the wire. When viewed from above, the induced current circles

• A.

Clockwise in both coils.

• B.

Counterclockwise in both coils.

• C.

Clockwise in the east coil and counterclockwise in the west coil.

• D.

Counterclockwise in the east coil and clockwise in the west coil.

D. Counterclockwise in the east coil and clockwise in the west coil.
Explanation
When an ever-increasing current flows northward through the long straight wire, it creates a magnetic field around it. According to Faraday's law of electromagnetic induction, this changing magnetic field induces an electric current in the coils of wire. The direction of the induced current can be determined using the right-hand rule. Applying the right-hand rule, we can see that the magnetic field lines from the long straight wire would cause the induced current to flow counterclockwise in the east coil and clockwise in the west coil. Therefore, the correct answer is counterclockwise in the east coil and clockwise in the west coil.

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• 14.

### A bar magnet falls through a loop of wire with the north pole entering first. As the north pole enters the wire, the induced current will be (as viewed from above)

• A.

Zero.

• B.

Clockwise.

• C.

Counterclockwise.

• D.

To top of loop.

C. Counterclockwise.
Explanation
When a bar magnet falls through a loop of wire with the north pole entering first, it creates a changing magnetic field. According to Faraday's law of electromagnetic induction, a changing magnetic field induces an electric current in a nearby conductor. In this case, the changing magnetic field induces a counterclockwise current in the wire. This can be explained by Lenz's law, which states that the induced current creates a magnetic field that opposes the change in the original magnetic field. Therefore, the induced current in the wire will flow counterclockwise to create a magnetic field that opposes the north pole entering the loop.

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• 15.

### A circular loop of wire is rotated at constant angular speed about an axis whose direction can be varied. In a region where a uniform magnetic field points straight down, what must be the orientation of the loop's axis of rotation if the induced emf is to be zero?

• A.

Any horizontal orientation will do.

• B.

It must make an angle of 45° to the vertical.

• C.

It must be vertical.

• D.

C. It must be vertical.
Explanation
The induced emf in a wire loop is zero when the magnetic field lines are perpendicular to the plane of the loop. In this case, the uniform magnetic field points straight down, so the loop's axis of rotation must be vertical in order to have zero induced emf.

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• 16.

### A circular loop of wire is rotated at constant angular speed about an axis whose direction can be varied. In a region where a uniform magnetic field points straight down, what must be the orientation of the loop's axis of rotation if the induced emf is to be a maximum?

• A.

Any horizontal orientation will do.

• B.

It must make an angle of 45° to the vertical.

• C.

It must be vertical.

• D.

A. Any horizontal orientation will do.
Explanation
The induced emf is a maximum when the magnetic field lines are perpendicular to the loop's plane. Since the magnetic field points straight down, any horizontal orientation of the loop's axis of rotation will result in the magnetic field being perpendicular to the loop, maximizing the induced emf. Therefore, any horizontal orientation will do.

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• 17.

### A wire moves across a magnetic field. The emf produced in the wire depends on

• A.

The strength of the magnetic field.

• B.

The length of the wire.

• C.

The orientation of the wire with respect to the magnetic field vector.

• D.

D. All of the given answers
Explanation
The emf produced in a wire moving across a magnetic field depends on multiple factors. The strength of the magnetic field affects the magnitude of the emf induced in the wire. The length of the wire also plays a role, as a longer wire will experience a greater change in magnetic flux and therefore a higher emf. Additionally, the orientation of the wire with respect to the magnetic field vector affects the angle at which the magnetic field lines cut across the wire, influencing the emf. Therefore, all of the given answers are correct as they all contribute to the emf produced in the wire.

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• 18.

### A horizontal rod (oriented in the east-west direction) is moved northward at constant velocity through a magnetic field that points straight down. Make a statement concerning the potential induced across the rod.

• A.

The west end of the rod is at higher potential than the east end.

• B.

The east end of the rod is at higher potential than the west end.

• C.

The top surface of the rod is at higher potential than the bottom surface.

• D.

The bottom surface of the rod is at higher potential than the top surface.

A. The west end of the rod is at higher potential than the east end.
Explanation
When a conductor moves through a magnetic field, a potential difference is induced across the conductor due to the interaction between the magnetic field and the moving charges in the conductor. According to the right-hand rule, the induced current flows in a direction that creates a magnetic field that opposes the change in the original magnetic field. In this case, as the rod moves northward, the induced current flows from west to east. Therefore, the west end of the rod, where the current enters, is at a higher potential than the east end, where the current exits.

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• 19.

### An electric generator transforms

• A.

Electrical energy into mechanical energy.

• B.

Mechanical energy into electrical energy.

• C.

Direct current into alternating current.

• D.

Alternating current into direct current.

B. Mechanical energy into electrical energy.
Explanation
An electric generator is a device that converts mechanical energy into electrical energy. It does this by using a magnetic field to induce an electric current in a wire coil. The mechanical energy can come from various sources such as a turbine driven by steam, water, or wind. As the coil rotates within the magnetic field, the changing magnetic field induces a current in the wire, producing electrical energy. Therefore, the correct answer is "mechanical energy into electrical energy."

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• 20.

### A generator coil rotates through 60 revolutions each second. The frequency of the emf is

• A.

30 Hz.

• B.

60 Hz.

• C.

120 Hz.

• D.

Cannot be determined from the information given.

B. 60 Hz.
Explanation
The frequency of the emf can be determined from the given information because it is stated that the generator coil rotates through 60 revolutions each second. The frequency of the emf is directly related to the number of revolutions per second, so if the coil rotates through 60 revolutions each second, the frequency of the emf is 60 Hz.

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• 21.

### A transformer is a device used to

• A.

Transform an alternating current into a direct current.

• B.

Transform a direct current into an alternating current.

• C.

Increase or decrease an ac voltage.

• D.

Increase or decrease a dc voltage.

C. Increase or decrease an ac voltage.
Explanation
A transformer is a device that is used to increase or decrease the voltage of an alternating current (AC). It does not convert AC to DC or vice versa. The primary purpose of a transformer is to change the voltage level of an AC power supply to a level suitable for transmission or distribution. This is achieved by the principle of electromagnetic induction, where the alternating current in the primary coil induces a current in the secondary coil, resulting in a change in voltage. Therefore, the correct answer is to increase or decrease an AC voltage.

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• 22.

### A transformer is a device that

• A.

Operates on either DC or AC

• B.

Operates only on AC.

• C.

Operates only on DC.

B. Operates only on AC.
Explanation
A transformer is a device that operates only on AC. This is because transformers work based on the principle of electromagnetic induction, which requires a changing magnetic field. In AC circuits, the current constantly changes direction, creating a changing magnetic field that allows the transformer to function. On the other hand, in DC circuits, the current flows in only one direction, resulting in a constant magnetic field that does not induce voltage in the secondary coil of the transformer. Therefore, transformers are specifically designed to operate with AC power sources.

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• 23.

### In a transformer, if the secondary coil contains more loops than the primary coil then it is a

• A.

Step-up transformer.

• B.

Step-down transformer.

A. Step-up transformer.
Explanation
A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. The primary coil is connected to the input voltage source, while the secondary coil is connected to the load. In a step-up transformer, the secondary coil has more loops than the primary coil, resulting in an increased output voltage compared to the input voltage. This allows the transformer to step up the voltage and is commonly used in power transmission systems to increase voltage levels for efficient long-distance transmission. Therefore, the correct answer is a step-up transformer.

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• 24.

### In a transformer, if the primary coil contains more loops than the secondary coil then it is a

• A.

Step-up transformer.

• B.

Step-down transformer.

B. Step-down transformer.
Explanation
A transformer is a device that transfers electrical energy between two or more circuits through electromagnetic induction. The primary coil is the coil that receives the electrical energy, and the secondary coil is the coil that transfers the energy to the load. In a step-up transformer, the secondary coil has more loops than the primary coil, resulting in an increase in voltage. Conversely, in a step-down transformer, the primary coil has more loops than the secondary coil, causing a decrease in voltage. Therefore, if the primary coil contains more loops than the secondary coil, it is a step-down transformer.

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• 25.

### In a transformer, the power input

• A.

Is larger than the power output.

• B.

) is equal to the power output.

• C.

Is smaller than the power output.

• D.

Can be either larger or smaller than the power output.

B. ) is equal to the power output.
Explanation
In a transformer, the power input is equal to the power output. This is because a transformer operates on the principle of energy conservation. The input power is used to create a magnetic field which induces a voltage in the secondary coil, resulting in the output power. The transformer is designed in such a way that the power is transferred efficiently from the primary to the secondary coil, without any significant losses. Therefore, the power input and output are equal in a transformer.

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• 26.

### In a given LC resonant circuit,

• A.

The stored electric field energy is greater than the stored magnetic field energy.

• B.

The stored electric field energy is less than the stored magnetic field energy.

• C.

The stored electric field energy is equal to the stored magnetic field energy.

• D.

All of the given answers are possible.

D. All of the given answers are possible.
Explanation
In a LC resonant circuit, the energy is stored in both the electric field and the magnetic field. The amount of energy stored in each field depends on the values of the inductance and capacitance in the circuit. Therefore, it is possible for the stored electric field energy to be greater than, less than, or equal to the stored magnetic field energy, depending on the specific values of the components in the circuit. Hence, all of the given answers are possible.

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• 27.

### A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the resistor is

• A.

Greater than the battery's terminal voltage.

• B.

Equal to the battery's terminal voltage.

• C.

Less than the battery's terminal voltage, but not zero.

• D.

Zero.

D. Zero.
Explanation
When a resistor and an inductor are connected in series to an ideal battery, the voltage across the inductor is initially zero due to its property of opposing changes in current. Therefore, the voltage across the resistor is also zero at the moment contact is made with the battery.

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• 28.

### A resistor and an inductor are connected in series to an ideal battery of constant terminal voltage. At the moment contact is made with the battery, the voltage across the inductor is

• A.

Greater than the battery's terminal voltage.

• B.

Equal to the battery's terminal voltage.

• C.

Less than the battery's terminal voltage, but not zero.

• D.

Zero.

B. Equal to the battery's terminal voltage.
Explanation
When a resistor and an inductor are connected in series to an ideal battery, the voltage across the inductor at the moment contact is made with the battery is equal to the battery's terminal voltage. This is because in an ideal circuit, there is no initial change in current, so the voltage across the inductor is equal to the voltage across the battery.

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• 29.

### A series RL circuit with inductance L and resistance R is connected to an emf V. After a period of time, the current reaches a final value of 2.0 A. A second series circuit is identical except that the inductance is 2L. When it is connected to the same emf V, what will be the final value of the current?

• A.

0.50 A

• B.

1.0 A

• C.

2.0 A

• D.

4.0 A

C. 2.0 A
Explanation
In a series RL circuit, the final value of the current is determined by the ratio of the inductance to the resistance (L/R). In this case, the second circuit has an inductance of 2L compared to the first circuit. Since the resistance is the same in both circuits, the ratio of inductance to resistance (L/R) is the same. Therefore, the final value of the current in the second circuit will also be 2.0 A.

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• 30.

### A resistor and an inductor are connected in series to a battery. The time constant for the circuit represents the time required for the current to reach

• A.

25% of the maximum current.

• B.

37% of the maximum current.

• C.

63% of the maximum current.

• D.

75% of the maximum current.

C. 63% of the maximum current.
Explanation
The time constant for an RL circuit represents the time required for the current to reach approximately 63% of the maximum current. This is because in an RL circuit, the time constant is equal to the inductance divided by the resistance (τ = L/R). The current in an RL circuit follows an exponential growth pattern, and it takes approximately 5 time constants for the current to reach its maximum value. At 1 time constant, the current is approximately 63% of the maximum value.

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• 31.

### A resistor and an inductor are connected in series to a battery. The battery is suddenly removed from the circuit. The time constant for of the circuit represents the time required for the current to decrease to

• A.

25% of the original value.

• B.

37% of the original value.

• C.

63% of the original value.

• D.

75% of the original value.

B. 37% of the original value.
Explanation
The time constant for an RL circuit is given by the formula τ = L/R, where L is the inductance and R is the resistance. When the battery is suddenly removed from the circuit, the current in the circuit starts to decrease. The time constant represents the time required for the current to decrease to approximately 37% of its original value. This is because after one time constant, the current decreases to approximately 37% of its initial value, and it continues to decrease exponentially from there. Therefore, the correct answer is 37% of the original value.

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• 32.

### All of the following have the same units except:

• A.

Inductance.

• B.

Capacitive reactance.

• C.

Impedance.

• D.

Resistance.

A. Inductance.
Explanation
The correct answer is inductance. This is because inductance is measured in units of henries (H), while capacitive reactance is measured in ohms (Ω), impedance is also measured in ohms (Ω), and resistance is also measured in ohms (Ω). Therefore, all of the other options have the same units (ohms), except for inductance.

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• 33.

### A resistor is connected to an AC power supply. On this circuit, the current

• A.

• B.

Lags the voltage by 90°.

• C.

Is in phase with the voltage.

• D.

C. Is in pHase with the voltage.
Explanation
When the current is in phase with the voltage, it means that they both reach their maximum and minimum values at the same time. This indicates that the resistor is purely resistive and does not introduce any phase shift between the current and voltage. In other words, the resistor does not store or release energy, and the power factor is equal to 1. Therefore, the correct answer is that the current is in phase with the voltage.

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• 34.

### A pure inductor is connected to an AC power supply. In this circuit, the current

• A.

• B.

Lags the voltage by 90°.

• C.

Is in phase with the voltage.

• D.

B. Lags the voltage by 90°.
Explanation
When a pure inductor is connected to an AC power supply, the current lags the voltage by 90°. This is because an inductor resists changes in current by inducing a voltage that opposes the change. As the voltage across the inductor changes, the current takes time to build up, causing it to lag behind the voltage. This lagging of the current by 90° is a characteristic behavior of inductive circuits.

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• 35.

### The inductive reactance in an ac circuit changes by what factor when the frequency is tripled?

• A.

1/3

• B.

1/9

• C.

3

• D.

9

C. 3
Explanation
When the frequency in an AC circuit is tripled, the inductive reactance changes by a factor of 3. This is because inductive reactance is directly proportional to the frequency of the AC signal. As the frequency increases, the inductive reactance also increases. Therefore, when the frequency is tripled, the inductive reactance will also triple.

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• 36.

### If the frequency of the AC voltage across an inductor is doubled, the inductive reactance of that inductor

• A.

Increases to 4 times its original value.

• B.

Increases to twice its original value.

• C.

Decreases to one-half its original value.

• D.

Decreases to one-fourth its original value.

B. Increases to twice its original value.
Explanation
When the frequency of the AC voltage across an inductor is doubled, the inductive reactance of the inductor increases to twice its original value. This is because inductive reactance is directly proportional to the frequency of the AC voltage. As the frequency doubles, the inductive reactance also doubles.

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• 37.

### As the frequency of the AC voltage across an inductor approaches zero, the inductive reactance of that coil

• A.

Approaches zero.

• B.

Approaches infinity.

• C.

Approaches unity.

• D.

A. Approaches zero.
Explanation
As the frequency of the AC voltage across an inductor approaches zero, the inductive reactance of that coil approaches zero. This is because inductive reactance is directly proportional to frequency. As the frequency decreases, the inductive reactance decreases as well, eventually approaching zero.

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• 38.

### A pure capacitor is connected to an AC power supply. In this circuit, the current

• A.

• B.

Lags the voltage by 90°.

• C.

Is in phase with the voltage.

• D.

A. Leads the voltage by 90°.
Explanation
In an AC circuit with a pure capacitor, the current leads the voltage by 90°. This is because in a capacitor, the current is directly proportional to the rate of change of voltage. As the voltage across the capacitor increases, the current flows in the opposite direction to charge the capacitor. As the voltage decreases, the current flows in the opposite direction to discharge the capacitor. This phase difference of 90° between the current and voltage is characteristic of a pure capacitor in an AC circuit.

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• 39.

### The capacitive reactance in an ac circuit changes by what factor when the frequency is tripled?

• A.

1/3

• B.

1/9

• C.

3

• D.

9

A. 1/3
Explanation
When the frequency in an AC circuit is tripled, the capacitive reactance decreases. This is because the capacitive reactance is inversely proportional to the frequency. Therefore, if the frequency is tripled, the capacitive reactance will be divided by 3. In other words, the capacitive reactance changes by a factor of 1/3 when the frequency is tripled.

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• 40.

### As the frequency of the AC voltage across a capacitor approaches zero, the capacitive reactance of that capacitor

• A.

Approaches zero.

• B.

Approaches infinity.

• C.

Approaches unity.

• D.

B. Approaches infinity.
Explanation
As the frequency of the AC voltage across a capacitor approaches zero, the capacitive reactance of that capacitor approaches infinity. This is because the capacitive reactance is inversely proportional to the frequency of the AC voltage. As the frequency approaches zero, the reactance becomes larger and larger, eventually becoming infinite. This means that at very low frequencies, the capacitor effectively blocks the flow of current, behaving like an open circuit.

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• 41.

### What is the phase angle between the voltages of the inductor and capacitor in a RLC series circuit?

• A.

Zero

• B.

90°

• C.

180°

• D.

270°

C. 180°
Explanation
In a RLC series circuit, the inductor and capacitor are connected in series. The inductor creates a voltage that leads the current by 90°, while the capacitor creates a voltage that lags the current by 90°. Since the inductor and capacitor voltages are opposite in phase, the phase angle between them is 180°.

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• 42.

### Consider an RLC circuit. The impedance of the circuit increases if R increases. When is this statement true?

• A.

Always true

• B.

True only if X_L is less than or equal to X_C

• C.

True only if X_L is greater than or equal to X_C

• D.

Never true

A. Always true
Explanation
In an RLC circuit, the impedance is given by the formula Z = √(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. The impedance increases when the value inside the square root increases. Since R is always positive, increasing R will always increase the impedance. Therefore, the statement "The impedance of the circuit increases if R increases" is always true.

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• 43.

### Consider an RLC circuit. The impedance of the circuit increases if X_L increases. When is this statement true?

• A.

Always true

• B.

True only if X_L is less than or equal to X_C

• C.

True only if X_L is greater than or equal to X_C

• D.

Never true

C. True only if X_L is greater than or equal to X_C
Explanation
In an RLC circuit, the impedance is given by Z = √(R^2 + (X_L - X_C)^2), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. The impedance increases when the term (X_L - X_C) increases. Therefore, the statement is true only if X_L is greater than or equal to X_C, because in this case, the difference (X_L - X_C) is positive and contributes to the increase in impedance.

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• 44.

### Consider an RLC series circuit. The impedance of the circuit increases if X_C increases. When is this statement true?

• A.

Always true

• B.

True only if X_L is less than or equal to X_C

• C.

True only if X_L is greater than or equal to X_C

• D.

Never true

B. True only if X_L is less than or equal to X_C
Explanation
In an RLC series circuit, the impedance is given by Z = R + j(X_L - X_C), where R is the resistance, X_L is the inductive reactance, and X_C is the capacitive reactance. The impedance increases if the imaginary part (X_L - X_C) increases. Therefore, the statement is true only if X_L is less than or equal to X_C. If X_L is greater than X_C, the imaginary part would be negative, causing the impedance to decrease.

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• 45.

### If the inductance and the capacitance both double in an LRC series circuit, the resonant frequency of that circuit will

• A.

Decrease to one-half its original value.

• B.

Decrease to one-fourth its original value.

• C.

Decrease to one-eighth its original value.

• D.

A. Decrease to one-half its original value.
Explanation
When the inductance and capacitance both double in an LRC series circuit, the resonant frequency is determined by the equation f = 1 / (2π√(LC)). If both L and C double, the denominator of the equation will also double. As a result, the resonant frequency will decrease to one-half its original value.

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• 46.

### Consider an RLC circuit that is driven by an AC applied voltage. At resonance,

• A.

The peak voltage across the capacitor is greater than the peak voltage across the inductor.

• B.

The peak voltage across the inductor is greater than the peak voltage across the capacitor.

• C.

The current is in phase with the driving voltage.

• D.

The peak voltage across the resistor is equal to the peak voltage across the inductor.

C. The current is in pHase with the driving voltage.
Explanation
At resonance in an RLC circuit driven by an AC applied voltage, the current is in phase with the driving voltage. This means that the current and voltage waveforms reach their maximum and minimum values at the same time. This occurs because at resonance, the reactance of the inductor and capacitor cancel each other out, resulting in a purely resistive circuit. As a result, the current and voltage are in phase, leading to the given answer.

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• 47.

### Resonance in a series RLC circuit occurs when

• A.

X_L is greater than X_C.

• B.

X_C is greater than X_L.

• C.

(X_L - X_C)2 is equal to R^2.

• D.

X_C equals X_L.

D. X_C equals X_L.
Explanation
In a series RLC circuit, resonance occurs when the reactance of the inductor (X_L) is equal to the reactance of the capacitor (X_C). This means that the impedance of the circuit is purely resistive, with no reactance. At resonance, the inductive and capacitive reactances cancel each other out, resulting in a balanced circuit. This is the condition where the circuit is most efficient and the current and voltage are in phase.

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• 48.

### A flux of 4.0 * 10^(-5) Wb is maintained through a coil for 0.50 s. What emf is induced in this coil by this flux?

• A.

8.0 * 10^(-5) V

• B.

4.0 * 10^(-5) V

• C.

2.0 * 10^(-5) V

• D.

D) No emf is induced in this coil.

D. D) No emf is induced in this coil.
• 49.

### A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are parallel.

• A.

Zero

• B.

3.1 * 10^(-3) T*m^2

• C.

5.5 * 10^(-3) T*m^2

• D.

6.3 * 10^(-3) T*m^2

A. Zero
Explanation
When the plane of the loop and the magnetic field vector are parallel, the angle between them is 0 degrees. The magnetic flux through a loop is given by the equation Φ = B*A*cos(θ), where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field vector and the normal to the loop. Since the angle is 0 degrees, the cosine of 0 degrees is 1, and therefore the magnetic flux through the loop is zero.

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• 50.

### A circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are perpendicular.

• A.

Zero

• B.

3.1 * 10^(-3) T*m^2

• C.

5.5 * 10^(-3) T*m^2

• D.

6.3 * 10^(-3) T*m^2

D. 6.3 * 10^(-3) T*m^2
Explanation
When the plane of the loop and the magnetic field vector are perpendicular, the magnetic flux through the loop is given by the formula Φ = B*A*cos(θ), where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field vector and the normal to the loop. Since the angle is 90 degrees, the cosine of 90 degrees is 0, resulting in a magnetic flux of zero. Therefore, the correct answer is zero.

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• Current Version
• Mar 21, 2023
Quiz Edited by
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• Oct 31, 2012
Quiz Created by
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