Free BEE Bachelor of Electrical Engineering DC and AC Circuit Analysis Questions and Answers — Questions and Answers
Question 1: According to Thevenin's theorem, any linear electrical network with two terminals can be replaced by an equivalent circuit consisting of what?
- A current source in parallel with a resistor
- A voltage source in series with a resistor (Correct answer)
- A voltage source in parallel with a capacitor
- A current source in series with an inductor
Correct answer: A voltage source in series with a resistor
Thevenin's theorem states that any linear circuit can be simplified to an equivalent circuit with a single voltage source (Vth) in series with a single resistor (Rth) connected to a load. This simplifies the analysis of the original complex circuit.
Question 2: In a series RLC circuit, what condition results in a critically damped response to a step input?
- (R/2L)^2 > 1/LC
- (R/2L)^2 < 1/LC
- (R/2L)^2 = 1/LC (Correct answer)
- R = 0
Correct answer: (R/2L)^2 = 1/LC
The transient response of a series RLC circuit is determined by the damping factor. A critically damped response, which returns to equilibrium as quickly as possible without oscillating, occurs when the damping ratio is equal to 1. This corresponds to the condition where (R/2L)^2 = 1/LC.
Question 3: A design engineer needs to correct the power factor of an industrial motor that presents a lagging (inductive) load. Which of the following is the most common and effective method to improve the power factor towards unity?
- Adding a resistor in series with the motor.
- Adding an inductor in parallel with the motor.
- Adding a capacitor in parallel with the motor. (Correct answer)
- Increasing the source voltage.
Correct answer: Adding a capacitor in parallel with the motor.
Inductive loads cause the current to lag the voltage, resulting in a poor (lagging) power factor. To correct this, a component that causes current to lead the voltage is needed. Capacitors have this property. By adding a capacitor in parallel with the inductive load, the leading reactive power from the capacitor compensates for the lagging reactive power of the motor, bringing the power factor closer to unity.
Question 4: For maximum power transfer in an AC circuit, what must be the relationship between the load impedance (ZL) and the Thevenin equivalent impedance (Zth) of the source network?
- ZL = Zth
- ZL = -Zth
- ZL is the reciprocal of Zth
- ZL is the complex conjugate of Zth (Correct answer)
Correct answer: ZL is the complex conjugate of Zth
The maximum power transfer theorem for AC circuits states that maximum power is delivered from a source to a load when the load impedance is the complex conjugate of the Thevenin (or source) impedance. If Zth = Rth + jXth, then for maximum power transfer, ZL must be Rth - jXth.
Question 5: When applying the superposition theorem to a circuit containing multiple independent sources, how are the other sources treated when calculating the contribution of a single voltage source?
- All other voltage sources are replaced by open circuits, and all current sources are replaced by short circuits.
- All other voltage sources are replaced by short circuits, and all current sources are replaced by open circuits. (Correct answer)
- All other sources are removed from the circuit entirely.
- All other sources are left in the circuit, but their values are set to zero.
Correct answer: All other voltage sources are replaced by short circuits, and all current sources are replaced by open circuits.
The superposition theorem allows for the analysis of a linear circuit with multiple sources by considering each source independently. When analyzing the effect of one voltage source, all other independent voltage sources are turned off (replaced by a short circuit, their ideal internal resistance) and all independent current sources are turned off (replaced by an open circuit, their ideal internal resistance).
Question 6: Which of the following statements accurately describes the relationship between a Thevenin equivalent circuit and a Norton equivalent circuit?
- They are completely independent and cannot be derived from one another.
- The Norton resistance is the reciprocal of the Thevenin resistance.
- They are duals of each other; a Norton equivalent can be derived from a Thevenin equivalent and vice-versa. (Correct answer)
- A Thevenin circuit is used for DC analysis, while a Norton circuit is used for AC analysis.
Correct answer: They are duals of each other; a Norton equivalent can be derived from a Thevenin equivalent and vice-versa.
Thevenin's theorem and Norton's theorem are considered duals. A Thevenin equivalent circuit (a voltage source Vth in series with a resistor Rth) can be converted into a Norton equivalent circuit (a current source In in parallel with a resistor Rn) and vice versa. The resistances are identical (Rth = Rn), and the sources are related by Ohm's law (Vth = In * Rn).
Free BEE Bachelor of Electrical Engineering DC and AC Circuit Analysis Questions and Answers
According to Thevenin's theorem, any linear electrical network with two terminals can be replaced by an equivalent circuit consisting of what?