Electrical Circuits (B) - Quiz 1

The given statement is false. A resonant circuit consists of both an inductor and a capacitor, along with a voltage or current source. The inductor and capacitor work together to create a resonant frequency at which the circuit can store and exchange energy efficiently. Without the presence of an inductor, the circuit would not exhibit resonance.

At resonance, the impedance of a circuit is at its minimum, which means that the current flowing through the circuit is maximum. According to the power formula (P = I^2 * R), when the current is maximum, the power is also maximum. Therefore, it is true that the power must be maximum at resonance.

The statement is true because in an ideal transformer, there are no losses associated with power transfer. This means that all the power supplied to the primary winding is transferred to the secondary winding without any losses due to resistance, hysteresis, or eddy currents. In an ideal transformer, the efficiency is 100%, meaning that the input power is equal to the output power. This makes ideal transformers highly efficient and desirable for various applications where power loss needs to be minimized.

Band pass filters and band reject filters are two different types of filters. A band pass filter allows a certain range of frequencies to pass through while attenuating frequencies outside that range. On the other hand, a band reject filter, also known as a notch filter, attenuates a specific range of frequencies while allowing all others to pass through. Therefore, band pass filters and band reject filters are not the same, making the statement false.

A filter that prevents a band of frequencies between two designated values is actually called a band-stop filter, not a high stop filter. A band-stop filter allows frequencies outside of the designated range to pass through while attenuating or blocking frequencies within the range. A high stop filter, on the other hand, is a filter that attenuates or blocks frequencies above a certain cutoff frequency. Therefore, the correct answer is False.

The power response of a series resonant circuit is determined by its selectivity, which refers to its ability to respond to a specific frequency while rejecting others. The selectivity curve of a series resonant circuit is bell-shaped, indicating that it has a peak response at the resonant frequency and gradually decreases as the frequency moves away from the resonant frequency. Therefore, the statement that the power response of a series resonant circuit has a bell-shaped curve called the selectivity curve is true.

The given statement is false. The Laplace Transform is actually a simpler method for solving transient equations. It is a mathematical technique that transforms a time-domain function into a complex frequency-domain function, making it easier to solve differential equations involving time-dependent variables. This transformation simplifies the equations and allows for the use of algebraic operations, making it a powerful tool in engineering and physics.

The given statement is false. A series RLC circuit with a DC supply is not considered a first-order circuit. A first-order circuit is characterized by a single energy storage element, such as a resistor or a capacitor. In a series RLC circuit, there are three energy storage elements: a resistor (R), an inductor (L), and a capacitor (C). Therefore, it is a second-order circuit.

At parallel resonance, the power factor is unity. This means that the current and voltage are in phase, resulting in an efficient transfer of power. At resonance, the reactive power is minimized, and the circuit behaves as if it only has resistive elements. Therefore, the power factor is equal to 1, indicating a balanced and efficient power transfer.

The statement "At low frequency Vout = 0" is not true for a low pass filter. In a low pass filter, low frequencies are allowed to pass through while high frequencies are attenuated. Therefore, at low frequencies, the output voltage (Vout) will not be zero. Hence, the correct answer is False.

The resonant circuit does not consist only of an inductor with a voltage or current source. A resonant circuit typically consists of an inductor and a capacitor connected in parallel or in series. This combination of components creates a circuit that can resonate at a specific frequency, allowing for efficient transfer of energy between the inductor and capacitor. Therefore, the statement is false.

When two coils are close to each other, the magnetic field produced by the current flowing through one coil is able to pass through the second coil, causing a magnetic flux that links the two coils together. This phenomenon is known as mutual inductance and is the basis for the functioning of transformers and other electromagnetic devices. Therefore, the statement is true.

The quality factor Q is indeed used to measure the sharpness of resonance in a resonant circuit. It is a dimensionless parameter that represents the efficiency of energy transfer in the circuit. A higher Q value indicates a sharper resonance, meaning that the circuit can store and release energy more effectively. Conversely, a lower Q value indicates a broader resonance, indicating a less efficient energy transfer. Therefore, the statement is true.

The complementary solution in electrical circuits refers to the transient solution. Transient solution represents the response of the circuit to sudden changes or disturbances, such as when a switch is turned on or off. It is characterized by decaying oscillations or exponential decay until the circuit reaches a steady-state. The complementary solution is a part of the overall solution to a circuit, which also includes the particular solution that represents the steady-state behavior. Therefore, the given answer, "True," is correct.

The given statement is false. The derivative of a sinusoidal source with respect to time is not equal to 1/jw. The correct expression for the derivative of a sinusoidal source is jw, where j represents the imaginary unit and w represents the angular frequency. Therefore, the given statement is incorrect.

In an RC series circuit with a DC supply, the transient current decays with time because of the presence of the resistor (R) in the circuit. When the circuit is first connected, the capacitor (C) charges up and allows current to flow through the circuit. However, as time passes, the capacitor discharges through the resistor, causing the current to decrease gradually. This decay in current is known as transient current decay. Therefore, the statement "the transient current decays with time" is true for an RC series circuit with a DC supply.

When the inductance from one coil can interfere with the operation of another adjacent component by means of electromagnetic induction, protection is indeed needed. This is because electromagnetic induction can induce unwanted voltage or current in nearby components, leading to interference and potential damage. Therefore, the correct answer is False.

At parallel resonance, the admittance consists of both conductance (G) and susceptance (B). The conductance represents the real part of the admittance and is equal to 1/2R, where R is the resistance. However, the susceptance represents the imaginary part of the admittance and is not zero at parallel resonance. Therefore, the statement that the admittance consists only of conductance G = 1/2R is false.

If the bandwidth of a circuit is kept very narrow, the circuit is said to have a high selectivity. This is because selectivity refers to the ability of a circuit to filter out unwanted signals and only allow a specific range of frequencies to pass through. When the bandwidth is narrow, the circuit becomes more selective and can effectively filter out unwanted frequencies. Therefore, the correct answer is False.

The statement is incorrect. Partial fraction decomposition is not an urgent step to solve transient current using differential equation method. It is a technique used to simplify and solve rational functions by breaking them down into simpler fractions. While it may be used in some cases to solve transient current problems, it is not a necessary or essential step in the process.

The statement is false because M21 actually relates the induced voltage in coil 2 to the current in coil 1, not the other way around. M21 is a mutual inductance coefficient that represents the coupling between two coils in an electromagnetic system. It quantifies how the changing current in one coil induces a voltage in the other coil.

In practical parallel resonance, if the internal resistance of the coil is negligible, it means that the coil does not contribute any significant resistance to the circuit. Therefore, the resonance frequency of the circuit will be equal to the resonant frequency of ideal parallel resonance, where there is no internal resistance. This is because the presence of internal resistance in the coil affects the behavior of the circuit and can shift the resonance frequency. However, if the internal resistance is negligible, it will not have a significant impact on the resonance frequency, making the statement true.

In dot convention, the direction of the current flow is represented by a dot on one end of the coil. If the currents enter the dotted terminals of two coils, it means that the currents are flowing in the same direction. In this case, the mutual inductance (M) between the two coils will be positive.

In series resonance, the quality factor of the resonant circuit must be high when the band of frequencies to be selected or rejected is narrow. This is because a high quality factor indicates a narrow bandwidth, meaning that the resonant circuit can effectively select or reject specific frequencies within a narrow range. Therefore, the statement is true.

The statement "At high frequency Vout = 0" is not true for a high pass filter. In a high pass filter, the output voltage increases as the frequency of the input signal increases. Therefore, at high frequencies, the output voltage will not be zero.

At parallel resonance, the magnitude of current in the reactive elements is higher than the applied source current, not lower. This is because at resonance, the reactive elements cancel out the reactive components of the source current, leading to a higher magnitude of current flowing through the reactive elements. Therefore, the statement that the magnitude of current in the reactive elements at parallel resonance is Q times lower than the applied source current is false.

Active filters do not consist of only passive elements R, L, and C. Active filters also include active components such as operational amplifiers or transistors to amplify or process the input signal. These active components allow for greater control and flexibility in shaping the frequency response of the filter. Therefore, the correct answer is False.

In a series resonant circuit, the phase of the current across the coil is not +90 when the supply is 5Sinωt. The phase depends on the frequency of the supply and the values of the inductance and capacitance in the circuit. Therefore, the statement is false.

At parallel resonance, the currents through the inductor and capacitor are not 90 degrees out of phase. In fact, at parallel resonance, the currents through the inductor and capacitor are in phase, meaning they have the same phase angle. This occurs because at resonance, the reactances of the inductor and capacitor cancel each other out, resulting in a purely resistive circuit. Therefore, the given statement is incorrect.

The statement suggests that the typical characteristics of a filter response curve are more sharp than ideal characteristics. However, the correct answer is False. In reality, the typical characteristics of a filter response curve are less sharp than ideal characteristics. Ideal characteristics refer to an ideal filter that has a perfectly sharp cutoff and no passband ripple, whereas real-world filters have some imperfections that cause a gradual transition between the passband and stopband.

In an RC series circuit with a DC supply, the transient current does not take the form of a triangle waveform. The transient current in an RC circuit follows an exponential decay curve. As the capacitor charges, the current decreases exponentially until it reaches a steady-state value. Therefore, the statement is false.

In an RC series circuit with a DC supply and a two-position switch, the boundary condition of the current in position two does not become 0 ampere. This means that the current does not completely stop flowing when the switch is in position two. Therefore, the statement is false.

The statement is true because a transformer is a device that utilizes mutual inductance to transfer electrical energy between two or more circuits. Mutual inductance occurs when the magnetic field produced by one coil induces a voltage in another coil. In a transformer, two coils, known as the primary and secondary windings, are wound around a common iron core. When an alternating current passes through the primary winding, it creates a changing magnetic field, which in turn induces a voltage in the secondary winding. This voltage can be stepped up or down depending on the number of turns in each winding, allowing for efficient power transmission and voltage transformation.

The statement is true because the mutual voltage between two components in a circuit can be either positive or negative. The sign of the mutual voltage depends on the relative orientation of the components and the direction of the current flow. If the current flows in the same direction through both components, the mutual voltage will be positive. If the current flows in opposite directions, the mutual voltage will be negative. Therefore, the mutual voltage can take on either positive or negative values.

In a step-down transformer, the number of turns in the secondary coil is less than the number of turns in the primary coil. This results in a lower voltage at the secondary coil compared to the primary coil. According to Ohm's Law (V = I * R), if the voltage decreases, the current must increase to maintain the same power. Therefore, the current at the secondary coil is greater than the primary coil.

When two loops, whether they have contacts between them or not, influence each other through the magnetic field produced by one of the loops, they are considered to be magnetically coupled. This means that changes in one loop's magnetic field can induce a current or voltage in the other loop. The statement is correct in stating that when this magnetic interaction occurs between the loops, they are magnetically coupled.

Second order filters contain two reactive elements, namely inductors (L) and capacitors (C). These reactive elements are used to create a circuit that can selectively pass or reject certain frequencies of an input signal. The combination of these reactive elements allows the filter to have a steeper roll-off and a higher degree of frequency selectivity compared to first order filters, which only contain one reactive element. Therefore, the statement that second order filters contain two reactive elements (L and C) is true.

The explanation for the given correct answer is that in an ideal transformer, the turns ratio is directly proportional to the square root of the self-inductance ratio. This means that as the self-inductance ratio increases, the turns ratio also increases. Therefore, the statement in the question is incorrect.

Passive filters are not necessarily more preferable than active filters. The choice between passive and active filters depends on the specific application and requirements. Passive filters are simpler and cheaper, but they have limitations in terms of frequency response and cannot amplify signals. Active filters, on the other hand, can provide amplification and have a wider range of frequency response. Therefore, the statement that passive filters are more preferable than active filters is false.

The statement is false because a steady state period is not obtained when a circuit is switched from one condition to another. A steady state refers to a condition in a circuit where all voltages and currents have reached a constant value and are not changing over time. When a circuit is switched from one condition to another, it goes through a transient period where the voltages and currents are changing before reaching a steady state.

The statement is true because according to Ohm's Law, the current flowing through a circuit is directly proportional to the voltage applied across it. Therefore, when there is a change in the applied voltage, the current in the circuit will also change. Additionally, changes in the circuit elements such as resistors, capacitors, or inductors can also affect the flow of current. Therefore, it is accurate to say that the current may vary in an electrical circuit when there is a change in the applied voltage or a change in one of the circuit elements.

The bandwidth of a resonant circuit refers to the range of frequencies over which the circuit can effectively deliver power. It is defined as the difference between the frequencies at which the circuit delivers half of the maximum power. This means that within the bandwidth, the circuit is able to efficiently transfer energy. Therefore, the statement is true.

At parallel resonance, the value of current will be maximum, not minimum. This is because at resonance, the total admittance is maximum, which means the impedance is minimum. According to Ohm's Law, current is inversely proportional to impedance. Therefore, when impedance is at its minimum, the current will be at its maximum.

The given statement is false. Band stop filters, also known as notch filters, are used to block or attenuate a certain band of frequencies while allowing all other frequencies to pass through. They are the opposite of band pass filters, which are used to pass a certain band of frequencies and attenuate all others.

The statement is true because differential equations and Laplace transforms are mathematical tools used to solve problems in various fields, including electrical engineering. When solving for transient current, both methods can yield the same solution. Differential equations describe the relationship between a function and its derivatives, while Laplace transforms convert a function of time into a function of complex frequency. In certain cases, applying the Laplace transform to a differential equation can simplify the problem and lead to the same solution as solving the original equation directly.

In a series RLC circuit with a DC supply, the transient current obtained is a part of the solution for the same circuit but with an AC supply. This is because the transient response of the circuit, which occurs when the circuit is switched on or off, can be considered as a superposition of the steady-state response to both the DC and AC components of the input. Therefore, the transient current can be seen as a portion of the solution for the circuit with an AC supply.

Passive filters are designed to attenuate or reduce certain frequencies in a signal, not to increase the voltage. Therefore, it is not possible for passive filters to generate an output voltage greater than the input voltage.

Mutual coupling exists when two or more circuits are physically close to each other and their magnetic or electric fields interact with each other. It is not dependent on whether the circuits are driven by time-constant sources or not. Therefore, the statement that mutual coupling exists when the circuits are driven by time-constant sources is false.

Mutual inductance, denoted by M, is a property of two adjacent coils or circuits that describes the ability of one coil to induce a voltage in the other coil. It is always positive because it represents the coupling between the coils, regardless of the direction of the induced voltage. Therefore, the statement that mutual inductance M may be negative is incorrect.

The RLC parallel resonant circuit does not provide a bandpass filter when the output is taken off the resistor. In this circuit configuration, the output is typically taken across the capacitor or inductor, not the resistor. The RLC parallel resonant circuit acts as a bandstop filter, also known as a notch filter, which attenuates a specific frequency or range of frequencies while allowing others to pass through.