# Chapter 19: DC Circuits

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• 1.

### The potential difference between the terminals of a battery, when no current flows to an external circuit, is referred to as the

• A.

Emf.

• B.

Terminal voltage.

A. Emf.
Explanation
The potential difference between the terminals of a battery, when no current flows to an external circuit, is referred to as the emf. This is because the emf (electromotive force) represents the maximum potential difference that the battery can provide, without any current being drawn from it. Terminal voltage, on the other hand, refers to the potential difference across the terminals of the battery when current is flowing through an external circuit. Therefore, in this context, the correct answer is emf.

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• 2.

### The potential difference between the terminals of a battery, when current flows to an external circuit, is referred to as the

• A.

Emf.

• B.

Terminal voltage.

B. Terminal voltage.
Explanation
When current flows through an external circuit connected to a battery, there is a potential difference between the terminals of the battery. This potential difference is known as the terminal voltage. It represents the voltage available to the external circuit for performing work. The terminal voltage may be less than the electromotive force (emf) of the battery due to internal resistance or other factors. Therefore, the correct answer is terminal voltage.

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• 3.

### When two or more resistors are connected in series to a battery

• A.

The total voltage across the combination is the algebraic sum of the voltages across the individual resistors.

• B.

The same current flows through each resistor.

• C.

The equivalent resistance of the combination is equal to the sum of the resistances of each resistor.

• D.

D. All of the given answers
Explanation
When two or more resistors are connected in series to a battery, the total voltage across the combination is the algebraic sum of the voltages across the individual resistors. This is because in a series circuit, the voltage is divided among the resistors in proportion to their resistance values. Additionally, the same current flows through each resistor in a series circuit, as there is only one path for the current to flow. Finally, the equivalent resistance of the combination is equal to the sum of the resistances of each resistor, as the total resistance in a series circuit is simply the sum of the individual resistances. Therefore, all of the given answers are correct.

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• 4.

### When resistors are connected in series,

• A.

The same power is dissipated in each one.

• B.

The potential difference across each is the same.

• C.

The current flowing in each is the same.

• D.

More than one of the given answers is true.

C. The current flowing in each is the same.
Explanation
When resistors are connected in series, the current flowing through each resistor is the same. This is because in a series circuit, there is only one path for the current to flow. Therefore, the current that enters one resistor must also pass through the other resistors in the circuit. As a result, the current remains constant throughout the series circuit, and each resistor experiences the same current flow.

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• 5.

### Three identical resistors are connected in series to a battery. If the current of 12 A flows from the battery, how much current flows through any one of the resistors?

• A.

12 A

• B.

4 A

• C.

36 A

• D.

Zero

A. 12 A
Explanation
When resistors are connected in series, the same current flows through each resistor. Since the current from the battery is 12 A, the current flowing through any one of the resistors will also be 12 A.

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• 6.

### Three identical resistors are connected in series to a 12-V battery. What is the voltage across any one of the resistors?

• A.

36 V

• B.

12 V

• C.

4 V

• D.

Zero

C. 4 V
Explanation
When resistors are connected in series, the total resistance is equal to the sum of individual resistances. In this case, since the resistors are identical, each resistor will have the same resistance. Therefore, the voltage across each resistor will be equal. Since the total voltage across the series circuit is 12 V, and there are 3 resistors, the voltage across each resistor will be 12 V divided by 3, which is equal to 4 V.

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• 7.

### You obtain a 100-W light bulb and a 50-W light bulb. Instead of connecting them in the normal way, you devise a circuit that places them in series across normal household voltage. Which statement is correct?

• A.

Both bulbs glow at the same reduced brightness.

• B.

Both bulbs glow at the same increased brightness.

• C.

The 100-W bulb glows brighter than the 50-W bulb.

• D.

The 50-W bulb glows more brightly than the 100-W bulb.

D. The 50-W bulb glows more brightly than the 100-W bulb.
Explanation
When the 100-W and 50-W light bulbs are connected in series across normal household voltage, the total resistance in the circuit increases. According to Ohm's Law (V = IR), when the resistance increases, the current flowing through the circuit decreases. Since both bulbs are connected in series, the same current flows through both of them. The power dissipated by a light bulb is given by P = IV, where P is power, I is current, and V is voltage. As the current decreases, the power dissipated by each bulb also decreases. Since the power of the 100-W bulb is higher than the 50-W bulb, it will glow less brightly compared to the 50-W bulb.

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• 8.

### As more resistors are added in series to a constant voltage source, the power supplied by the source

• A.

Increases.

• B.

Decreases.

• C.

Does not change.

• D.

Increases for a time and then starts to decrease.

B. Decreases.
Explanation
When resistors are added in series to a constant voltage source, the total resistance in the circuit increases. According to Ohm's Law (V = IR), if the resistance increases and the voltage stays constant, the current flowing through the circuit will decrease. Since power is calculated using the formula P = IV, where I is the current, a decrease in current will result in a decrease in power supplied by the source. Therefore, as more resistors are added in series, the power supplied by the source decreases.

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• 9.

### When two or more resistors are connected in parallel to a battery,

• A.

The voltage across each resistor is the same.

• B.

The total current flowing from the battery equals the sum of the currents flowing through each resistor.

• C.

The equivalent resistance of the combination is less than the resistance of any one of the resistors.

• D.

D. All of the given answers
Explanation
When two or more resistors are connected in parallel to a battery, all of the given answers are correct. The voltage across each resistor is the same because they are connected in parallel, meaning they have the same potential difference. The total current flowing from the battery equals the sum of the currents flowing through each resistor because in a parallel circuit, the current is divided among the branches. The equivalent resistance of the combination is less than the resistance of any one of the resistors because the total resistance decreases when resistors are connected in parallel.

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• 10.

### When resistors are connected in parallel, we can be certain that

• A.

The same current flows in each one.

• B.

The potential difference across each is the same.

• C.

The power dissipated in each is the same.

• D.

Their equivalent resistance is greater than the resistance of any one of the individual resistances.

B. The potential difference across each is the same.
Explanation
When resistors are connected in parallel, the potential difference across each resistor is the same. This is because the voltage across the entire parallel combination of resistors is the same, and according to Ohm's Law (V = IR), the potential difference across each resistor is directly proportional to its resistance. Therefore, when resistors are connected in parallel, the potential difference across each resistor remains constant.

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• 11.

### Three identical resistors are connected in parallel to a 12-V battery. What is the voltage of any one of the resistors?

• A.

36 V

• B.

12 V

• C.

4 V

• D.

Zero

B. 12 V
Explanation
When resistors are connected in parallel, the voltage across each resistor is the same. In this case, the three identical resistors are connected in parallel to a 12-V battery. Therefore, the voltage across any one of the resistors will also be 12 V.

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• 12.

### Three identical resistors are connected in parallel to a battery. If the current of 12 A flows from the battery, how much current flows through any one of the resistors?

• A.

12 A

• B.

4 A

• C.

36 A

• D.

Zero

B. 4 A
Explanation
When resistors are connected in parallel, the total current is divided equally among them. In this case, since the resistors are identical, the current will be divided equally among them. Therefore, if the total current from the battery is 12 A, each resistor will have a current of 4 A flowing through it.

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• 13.

### The lamps in a string of Christmas tree lights are connected in parallel. What happens if one lamp burns out? (Assume negligible resistance in the wires leading to the lamps.)

• A.

The brightness of the lamps will not change appreciably.

• B.

The other lamps get brighter equally.

• C.

The other lamps get brighter, but some get brighter than others.

• D.

The other lamps get dimmer equally.

• E.

The other lamps get dimmer, but some get dimmer than others.

A. The brightness of the lamps will not change appreciably.
Explanation
When the lamps in a string of Christmas tree lights are connected in parallel, each lamp has its own separate current path. Therefore, if one lamp burns out, it will not affect the flow of current to the other lamps. As a result, the brightness of the other lamps will not change appreciably.

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• 14.

### As more resistors are added in parallel to a constant voltage source, the power supplied by the source

• A.

Increases.

• B.

Decreases.

• C.

Does not change.

• D.

Increases for a time and then starts to decrease.

A. Increases.
Explanation
When resistors are added in parallel to a constant voltage source, the total resistance decreases. According to Ohm's Law (V = IR), if the resistance decreases, the current flowing through the circuit increases. Since power is calculated as P = IV, where I is the current and V is the voltage, an increase in current results in an increase in power supplied by the source. Therefore, as more resistors are added in parallel to a constant voltage source, the power supplied by the source increases.

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• 15.

### Consider three identical resistors, each of resistance R. The maximum power each can dissipate is P. Two of the resistors are connected in series, and a third is connected in parallel with these two. What is the maximum power this network can dissipate?

• A.

2P/3

• B.

3P/2

• C.

2P

• D.

3P

B. 3P/2
Explanation
When two resistors are connected in series, the total resistance is equal to the sum of their individual resistances. When a third resistor is connected in parallel with these two, the total resistance decreases. According to the power formula P = V^2/R, where V is the voltage, we can see that the power dissipated is inversely proportional to the resistance. Therefore, when the total resistance decreases, the power dissipated increases. Since the third resistor is connected in parallel, the total resistance decreases, resulting in an increase in power dissipated. Therefore, the maximum power this network can dissipate is 3P/2.

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• 16.

### Kirchhoff's loop rule is an example of

• A.

Conservation of energy.

• B.

Conservation of charge.

• C.

Conservation of momentum.

• D.

A. Conservation of energy.
Explanation
Kirchhoff's loop rule, also known as Kirchhoff's voltage law, states that the sum of the potential differences (voltages) around any closed loop in an electrical circuit is equal to zero. This rule is derived from the principle of conservation of energy, as it implies that the total energy supplied by the voltage sources in the circuit is equal to the total energy consumed by the resistors and other components in the circuit. Therefore, the correct answer is conservation of energy.

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• 17.

### Kirchhoff's junction rule is an example of

• A.

Conservation of energy.

• B.

Conservation of charge.

• C.

Conservation of momentum.

• D.

B. Conservation of charge.
Explanation
Kirchhoff's junction rule states that the total current entering a junction in an electrical circuit is equal to the total current leaving the junction. This principle is based on the conservation of charge, as charge cannot be created or destroyed, only transferred. Therefore, the correct answer is conservation of charge.

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• 18.

### If you connect two identical storage batteries together in series ("+" to "-" to "+" to "-"), and place them in a circuit, the combination will provide

• A.

Zero volts.

• B.

Twice the voltage, and different currents will flow through each.

• C.

Twice the voltage, and the same current will flow through each.

• D.

The same voltage, and different currents will flow through each.

C. Twice the voltage, and the same current will flow through each.
Explanation
When two identical storage batteries are connected in series, the positive terminal of one battery is connected to the negative terminal of the other battery. This arrangement increases the total voltage across the batteries, resulting in twice the voltage compared to a single battery. However, since the batteries are identical and connected in series, the same current will flow through each battery. This is because the current in a series circuit is constant throughout, so the current flowing through one battery is the same as the current flowing through the other battery.

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• 19.

### If you connect two identical storage batteries together in series ("+" to "-" to "-" to "+"), and place them in a circuit, the combination will provide

• A.

Zero volts.

• B.

Twice the voltage, and different currents will flow through each.

• C.

Twice the voltage, and the same current will flow through each.

• D.

The same voltage, and different currents will flow through each.

A. Zero volts.
Explanation
When two identical storage batteries are connected in series, the positive terminal of one battery is connected to the negative terminal of the other battery. This arrangement creates a closed loop circuit with no voltage difference across the two batteries. As a result, the combination will provide zero volts.

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• 20.

### If you connect two identical storage batteries together in parallel, and place them in a circuit, the combination will provide

• A.

Twice the voltage and twice the total charge that one battery would.

• B.

Twice the voltage and the same total charge that one battery would.

• C.

The same voltage and twice the total charge that one battery would.

• D.

D) half the voltage and half the total charge that one battery would.

C. The same voltage and twice the total charge that one battery would.
Explanation
When two identical storage batteries are connected together in parallel, the voltage across each battery remains the same. This is because the voltage is determined by the chemical reactions happening inside the battery, and connecting batteries in parallel does not change these reactions. However, the total charge provided by the combination of batteries is doubled. This is because when batteries are connected in parallel, their individual charges add up. Therefore, the combination will provide the same voltage as one battery but twice the total charge.

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• 21.

### When two or more capacitors are connected in series to a battery

• A.

The total voltage across the combination is the algebraic sum of the voltages across the individual capacitors.

• B.

Each capacitor carries the same amount of charge.

• C.

The equivalent capacitance of the combination is less than the capacitance of any of the capacitors.

• D.

D. All of the given answers
Explanation
When two or more capacitors are connected in series to a battery, all of the given answers are true. The total voltage across the combination is the algebraic sum of the voltages across the individual capacitors, meaning that the voltages add up. Each capacitor carries the same amount of charge, as the charge is shared among the capacitors. The equivalent capacitance of the combination is less than the capacitance of any of the capacitors, as the total capacitance decreases when capacitors are connected in series. Therefore, all of the given answers are correct.

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• 22.

### As more and more capacitors are connected in series, the equivalent capacitance of the combination increases.

• A.

Always true

• B.

Sometimes true; it depends on the voltage of the battery to which the combination is connected.

• C.

Sometimes true; it goes up only if the next capacitor is larger than the average of the existing combination.

• D.

Never true

D. Never true
Explanation
The statement says that as more and more capacitors are connected in series, the equivalent capacitance of the combination increases. However, this statement is never true. In a series combination of capacitors, the equivalent capacitance is always less than the smallest capacitance in the combination. This is because the total capacitance is limited by the smallest capacitor, as it restricts the flow of charge. Therefore, the statement is incorrect.

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• 23.

### Three identical capacitors are connected in series to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

• A.

3Q

• B.

Q

• C.

Q/3

• D.

Q/9

B. Q
Explanation
When three identical capacitors are connected in series, the total charge is divided equally among them. Since a total charge of Q flows from the battery, each capacitor carries a charge of Q.

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• 24.

### When two or more capacitors are connected in parallel to a battery,

• A.

The voltage across each capacitor is the same.

• B.

Each capacitor carries the same amount of charge.

• C.

The equivalent capacitance of the combination is less than the capacitance of any one of the capacitors.

• D.

A. The voltage across each capacitor is the same.
Explanation
When capacitors are connected in parallel to a battery, the voltage across each capacitor is the same. This is because in a parallel circuit, the voltage across each component is equal to the voltage across the battery. Therefore, all the capacitors connected in parallel will have the same voltage across them.

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• 25.

### As more and more capacitors are connected in parallel, the equivalent capacitance of the combination increases.

• A.

Always true

• B.

Sometimes true; it depends on the voltage of the battery to which the combination is connected.

• C.

Sometimes true; it goes up only if the next capacitor is larger than the average of the existing combination.

• D.

Never true

A. Always true
Explanation
When capacitors are connected in parallel, the total capacitance is the sum of the individual capacitances. This means that as more and more capacitors are added in parallel, the total capacitance of the combination increases. Therefore, the statement "As more and more capacitors are connected in parallel, the equivalent capacitance of the combination increases" is always true.

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• 26.

### Three identical capacitors are connected in parallel to a battery. If a total charge of Q flows from the battery, how much charge does each capacitor carry?

• A.

3Q

• B.

Q

• C.

Q/3

• D.

Q/9

C. Q/3
Explanation
When capacitors are connected in parallel, the total charge is divided equally among them. Since there are three identical capacitors in this case, the total charge Q will be divided equally among them, resulting in each capacitor carrying a charge of Q/3.

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• 27.

### What is the unit for the quantity RC?

• A.

Ohms

• B.

Volt-ampere/ohm

• C.

Seconds

• D.

Meters

C. Seconds
Explanation
The unit for the quantity RC is seconds. This is because RC represents the time constant in an RC circuit, which is the time it takes for the voltage across the capacitor to reach approximately 63.2% of its final value after a voltage is applied. The time constant is determined by the product of the resistance (R) and the capacitance (C) in the circuit, and its unit is therefore seconds.

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• 28.

### A resistor and a capacitor 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 capacitor is

• A.

Greater than the battery's terminal voltage.

• B.

Less than the battery's terminal voltage, but greater than zero.

• C.

Equal to the battery's terminal voltage.

• D.

Zero.

D. Zero.
Explanation
When the resistor and capacitor are connected in series to the battery, the capacitor initially acts as an open circuit. This means that no current can flow through the circuit, and therefore no voltage is dropped across the capacitor. As a result, the voltage across the capacitor is zero at the moment contact is made with the battery.

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• 29.

### A resistor and a capacitor 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.

Less than the battery's terminal voltage, but greater than zero.

• C.

Equal to the battery's terminal voltage.

• D.

Zero.

C. Equal to the battery's terminal voltage.
Explanation
When a resistor and a capacitor are connected in series to an ideal battery, the voltage across each component is the same. This is because in a series circuit, the total voltage of the battery is divided among the components. Therefore, at the moment contact is made with the battery, the voltage across the resistor is equal to the battery's terminal voltage.

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• 30.

### A resistor and a capacitor are connected in series to an ideal battery of constant terminal voltage. When this system reaches its steady-state, the voltage across the resistor is

• A.

Greater than the battery's terminal voltage.

• B.

Less than the battery's terminal voltage, but greater than zero.

• C.

Equal to the battery's terminal voltage.

• D.

Zero.

D. Zero.
Explanation
When a resistor and a capacitor are connected in series to an ideal battery, the capacitor charges up and reaches its maximum charge, while the current flowing through the resistor decreases over time. In the steady-state, the capacitor acts as an open circuit, meaning that no current flows through it. Therefore, all the voltage from the battery is dropped across the capacitor, resulting in zero voltage across the resistor. Hence, the voltage across the resistor is zero.

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• 31.

### An ideal ammeter should

• A.

Have a high coil resistance.

• B.

Introduce a very small series resistance into the circuit whose current is to be measured.

• C.

Introduce a very large series resistance into the circuit whose current is to be measured.

• D.

Consist of a galvanometer in series with a large resistor.

B. Introduce a very small series resistance into the circuit whose current is to be measured.
Explanation
An ideal ammeter should introduce a very small series resistance into the circuit whose current is to be measured because it should have a negligible effect on the circuit and not significantly alter the current being measured. By having a small series resistance, the ammeter will have a minimal impact on the circuit's overall resistance and will provide an accurate measurement of the current flowing through it.

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• 32.

### A galvanometer can be converted to an ammeter by the addition of a

• A.

Small resistance in parallel.

• B.

Large resistance in parallel.

• C.

Small resistance in series.

• D.

Large resistance in series.

A. Small resistance in parallel.
Explanation
When a small resistance is added in parallel to a galvanometer, it creates a new path for the current to flow through. This effectively diverts some of the current away from the galvanometer, allowing it to measure larger currents without being damaged. By adding a small resistance in parallel, the galvanometer becomes an ammeter, which is used to measure current.

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• 33.

### A current reading is obtained by properly placing an ammeter in a circuit consisting of one resistor and one battery. As a result,

• A.

The voltage drop across the resistor increases.

• B.

The current flowing in the circuit increases.

• C.

The current flowing in the circuit decreases.

• D.

The current flowing in the circuit does not change.

C. The current flowing in the circuit decreases.
Explanation
When an ammeter is properly placed in a circuit, it creates a parallel path for the current to flow through. This means that some of the current is diverted away from the resistor and through the ammeter. As a result, the current flowing through the resistor decreases, leading to a decrease in the overall current flowing in the circuit.

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• 34.

### Decreasing the resistance of an ammeter's shunt resistance

• A.

Allows it to measure a larger current at full scale deflection.

• B.

Allows it to measure a smaller current at full scale deflection.

• C.

Enables more current to pass directly through the galvanometer.

• D.

Converts it to a voltmeter.

A. Allows it to measure a larger current at full scale deflection.
Explanation
Decreasing the resistance of an ammeter's shunt resistance allows it to measure a larger current at full scale deflection because the shunt resistance is connected in parallel with the ammeter. By decreasing the resistance of the shunt, more current is diverted through the shunt, bypassing the majority of the current through the ammeter. This effectively increases the range of the ammeter, allowing it to measure larger currents without overloading the instrument.

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• 35.

### In order to construct a voltmeter from a galvanometer, one normally would

• A.

Use a very small shunt resistor.

• B.

Use a very large shunt resistor.

• C.

Use a very small series resistor.

• D.

Use a very large series resistor.

D. Use a very large series resistor.
Explanation
To construct a voltmeter from a galvanometer, a very large series resistor is used. This is because a voltmeter is designed to measure voltage across a circuit, which requires the least amount of current to flow through the meter. By using a very large series resistor, the majority of the current is forced to flow through the resistor instead of the galvanometer, allowing for accurate voltage measurements without damaging the galvanometer.

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• 36.

### Increasing the resistance of a voltmeter's series resistance

• A.

Allows it to measure a larger voltage at full-scale deflection.

• B.

Allows it to measure a smaller voltage at full-scale deflection.

• C.

Enables more current to pass through the meter movement at full-scale deflection.

• D.

Converts it to an ammeter.

A. Allows it to measure a larger voltage at full-scale deflection.
Explanation
Increasing the resistance of a voltmeter's series resistance allows it to measure a larger voltage at full-scale deflection because the series resistance limits the amount of current flowing through the voltmeter. By increasing the resistance, the current flowing through the voltmeter decreases, allowing it to measure higher voltages without exceeding its maximum current rating. As a result, the voltmeter can accurately measure larger voltages without causing damage to the instrument.

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• 37.

### A voltage reading is obtained by placing a voltmeter across a resistor. What happens to the total current flowing in the circuit as a result of this action?

• A.

The current increases.

• B.

The current decreases.

• C.

The current does not change.

• D.

The current increases if the meter's internal resistance is less than the original resistance in the circuit and decreases if its internal resistance is greater than the circuit's original resistance.

A. The current increases.
Explanation
When a voltmeter is placed across a resistor, it measures the voltage drop across that resistor. According to Ohm's Law, voltage and current are directly proportional, so an increase in voltage across the resistor would result in an increase in current flowing through it. Therefore, the total current flowing in the circuit would increase as a result of this action.

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• 38.

### An unknown resistor is wired in series with an ammeter, and a voltmeter is placed in parallel across both the resistor and the ammeter. This network is then placed across a battery. If one computes the value of the resistance by dividing the voltmeter reading by the ammeter reading, the value obtained

• A.

Is less than the true resistance.

• B.

Is greater than the true resistance.

• C.

Is the true resistance.

• D.

Could be any of the given answers. It depends on other factors.

B. Is greater than the true resistance.
Explanation
When an ammeter is connected in series with a resistor and a voltmeter is connected in parallel across both, the voltmeter will measure the total voltage across both the resistor and the ammeter. However, the ammeter will only measure the current passing through the resistor. This means that the voltmeter reading will be higher than the actual voltage across the resistor alone. When the voltmeter reading is divided by the ammeter reading, the resulting value will be higher than the actual resistance of the unknown resistor, leading to the conclusion that the value obtained is greater than the true resistance.

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• 39.

### An unknown resistor is wired in series with an ammeter, and a voltmeter is placed in parallel across the resistor only. This network is then connected to a battery. If one computes the value of the resistance by dividing the voltmeter reading by the ammeter reading, the value obtained

• A.

Is less than the true resistance.

• B.

Is greater than the true resistance.

• C.

Is the true resistance.

• D.

Could be any of the given answers. It depends on other factors.

A. Is less than the true resistance.
Explanation
When an ammeter is connected in series with the unknown resistor, it measures the total current passing through the circuit. However, when a voltmeter is connected in parallel across the resistor, it measures the voltage drop across the resistor only. The voltmeter reading divided by the ammeter reading gives the value of resistance. Since the voltmeter measures the voltage across the resistor only and not the total voltage of the circuit, the calculated resistance will be less than the true resistance of the unknown resistor.

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• 40.

### Four 20-Ω resistors are connected in series. What is the equivalent resistance?

• A.

80 Ω

• B.

20 Ω

• C.

10 Ω

• D.

5.0 Ω

A. 80 Ω
Explanation
When resistors are connected in series, their resistances add up. Since there are four 20-Ω resistors connected in series, the equivalent resistance is 20 Ω + 20 Ω + 20 Ω + 20 Ω = 80 Ω.

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• 41.

### Four resistors of 12, 3.0, 5.0, and 4.0 Ω are connected in series. A 12-V battery is connected to the combination. What is the current through the battery?

• A.

0.50 A

• B.

1.0 A

• C.

1.5 A

• D.

2.0 A

A. 0.50 A
Explanation
When resistors are connected in series, the total resistance is equal to the sum of the individual resistances. In this case, the total resistance is 12 + 3.0 + 5.0 + 4.0 = 24.0 Ω.

According to Ohm's Law, the current (I) flowing through a circuit is equal to the voltage (V) divided by the resistance (R). In this case, the voltage is 12 V and the resistance is 24.0 Ω.

Using the formula I = V/R, we can calculate the current as 12/24.0 = 0.50 A. Therefore, the current through the battery is 0.50 A.

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• 42.

### Three resistors of 12, 12, and 6.0 Ω are connected in series. A 12-V battery is connected to the combination. What is the current through the battery?

• A.

0.10 A

• B.

0.20 A

• C.

0.30 A

• D.

0.40 A

D. 0.40 A
Explanation
When resistors are connected in series, the total resistance is the sum of the individual resistances. In this case, the total resistance is 12 + 12 + 6 = 30 Ω. According to Ohm's Law, the current (I) can be calculated by dividing the voltage (V) by the resistance (R): I = V/R. Plugging in the values, we get I = 12 V / 30 Ω = 0.40 A. Therefore, the current through the battery is 0.40 A.

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• 43.

### Three resistors of 12, 12, and 6.0 Ω are connected in parallel. A 12-V battery is connected to the combination. What is the current through the 6.0-Ω resistor?

• A.

1.0 A

• B.

2.0 A

• C.

3.0 A

• D.

4.0 A

B. 2.0 A
Explanation
When resistors are connected in parallel, the total resistance is given by the formula 1/Rt = 1/R1 + 1/R2 + 1/R3. In this case, the total resistance is 1/12 + 1/12 + 1/6 = 1/4. The current through the circuit is given by Ohm's Law, I = V/R, where V is the voltage and R is the resistance. In this case, the voltage is 12 V and the total resistance is 1/4. Therefore, the current through the circuit is 12/(1/4) = 48 A. Since the 6.0-Ω resistor is one of the resistors in parallel, the current through it is the same as the total current, which is 48 A. Therefore, the current through the 6.0-Ω resistor is 2.0 A.

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• 44.

### A 14-A current flows into a series combination of a 3.0-Ω and a 4.0-Ω resistor. What is the voltage drop across the 4.0-Ω resistor?

• A.

38 V

• B.

42 V

• C.

56 V

• D.

98 V

C. 56 V
Explanation
In a series circuit, the total resistance is equal to the sum of the individual resistances. In this case, the total resistance is 3.0 Ω + 4.0 Ω = 7.0 Ω. The voltage drop across each resistor in a series circuit is proportional to its resistance. Using Ohm's Law (V = I * R), the voltage drop across the 4.0 Ω resistor can be calculated as 14 A * 4.0 Ω = 56 V. Therefore, the correct answer is 56 V.

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• 45.

### A 14-A current flows into a series combination of a 3.0-Ω and a 4.0-Ω resistor. What is the voltage drop across the 3.0-Ω resistor?

• A.

42 V

• B.

56 V

• C.

98 V

• D.

38 V

A. 42 V
Explanation
The voltage drop across a resistor can be calculated using Ohm's Law, which states that V = I * R, where V is the voltage, I is the current, and R is the resistance. In this case, the current flowing through the series combination of the 3.0-Ω and 4.0-Ω resistors is 14 A. Therefore, the voltage drop across the 3.0-Ω resistor can be calculated as V = 14 A * 3.0 Ω = 42 V.

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• 46.

### A 22-A current flows into a parallel combination of 4.0 Ω, 6.0 Ω, and 12 Ω resistors. What current flows through the 12-Ω resistor?

• A.

18 A

• B.

11 A

• C.

7.3 A

• D.

3.7 A

D. 3.7 A
Explanation
When current flows through a parallel combination of resistors, the total current is divided among the resistors based on their individual resistance values. The current flowing through each resistor can be calculated using the formula I = V/R, where I is the current, V is the voltage, and R is the resistance. In this case, the current flowing through the 12-Ω resistor can be calculated as I = 22 A * (12 Ω / (4 Ω + 6 Ω + 12 Ω)) = 3.7 A.

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• 47.

### A 22-A current flows into a parallel combination of a 4.0-Ω, 6.0-Ω, and 12-Ω resistors. What current flows through the 6.0-Ω resistor?

• A.

18 A

• B.

11 A

• C.

7.3 A

• D.

3.7 A

C. 7.3 A
Explanation
In a parallel combination of resistors, the total current entering the combination is divided among the individual resistors. The current flowing through each resistor is inversely proportional to its resistance. In this case, the 6.0-Ω resistor has a higher resistance compared to the 4.0-Ω and 12-Ω resistors. Therefore, it will have a lower current flowing through it. The correct answer, 7.3 A, is the current flowing through the 6.0-Ω resistor.

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• 48.

### A 22-A current flows into a parallel combination of a 4.0-Ω, 6.0-Ω, and 12-Ω resistor. What current flows through the 4.0-Ω resistor?

• A.

18 A

• B.

11 A

• C.

7.3 A

• D.

3.7 A

B. 11 A
Explanation
In a parallel circuit, the voltage across each resistor is the same, but the current is divided among the resistors. Using the formula I = V/R, where I is the current, V is the voltage, and R is the resistance, we can calculate the current flowing through the 4.0-Ω resistor. Since the current flowing into the parallel combination is 22 A, and the total resistance is 4.0 Ω + 6.0 Ω + 12 Ω = 22 Ω, we can use the formula I = V/R to find the voltage across the parallel combination, which is 22 A * 22 Ω = 484 V. Then, using the same formula, we can find the current flowing through the 4.0-Ω resistor, which is 484 V / 4.0 Ω = 121 A. Therefore, the correct answer is 11 A.

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• 49.

### A 6.0-Ω and a 12-Ω resistor are connected in parallel to a 36-V battery. What power is dissipated by the 6.0-Ω resistor?

• A.

220 W

• B.

48 W

• C.

490 W

• D.

24 W

A. 220 W
Explanation
When resistors are connected in parallel, the voltage across each resistor is the same. In this case, the voltage across the 6.0-Ω resistor is 36 V. To find the power dissipated by the resistor, we can use the formula P = V^2/R, where P is the power, V is the voltage, and R is the resistance. Plugging in the values, we get P = (36^2)/6.0 = 216/6.0 = 36 W. Therefore, the power dissipated by the 6.0-Ω resistor is 36 W, not 220 W.

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• 50.

### The following three appliances are connected to a 120-V circuit: 1200-W toaster, 650-W coffee pot, and 600-W microwave. If all were operated at the same time what total current would they draw?

• A.

4.0 A

• B.

5.0 A

• C.

10 A

• D.

20 A

D. 20 A
Explanation
When appliances are connected in parallel, the total current drawn is equal to the sum of the individual currents. In this case, the toaster draws a current of 10 A (1200 W / 120 V), the coffee pot draws a current of 5.42 A (650 W / 120 V), and the microwave draws a current of 5 A (600 W / 120 V). Adding these currents together gives a total current of 20.42 A, which can be rounded to 20 A. Therefore, the correct answer is 20 A.

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• Mar 19, 2023
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• Oct 15, 2012
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