51. Among the following, which is the right formula for decay in an inductive circuit?
A. i = I(1 − e − t/time constant)
B. i = I(1 − et /time constant)
C. i = (1 − e − t /time constant)
D. i = I(e − t /time constant)
Answer: D
The correct formula for decay in an inductive circuit is i = I(e − t /time constant).
As the time increases, the current in the inductor decreases and the voltage also increases.
52. The discharging time constant of a circuit consisting of an inductor is the time taken for the voltage in the inductor to become __________ % of the initial voltage.
A. 33
B. 63
C. 37
D. 36
Answer: C
We know that: V = V0(e − tR/L).
When t = L/R
we have: V = V0(e − 1) = 0.37 × V0.
Hence the time constant is the time taken for the voltage in an inductive circuit to become 0.37 times its initial voltage.
53. A coil has a resistance of 4 ohms and an inductance of 2H. It is connected to a 20V dc supply. Calculate the initial value of the voltage across the inductor.
A. 5V
B. 10V
C. 0 V
D. 20V
Answer: D
Initially, the inductor behaves as an open circuit for dc current so, V = V0 = 20V i.e. same as a voltage source.
54. A coil has a resistance of 4 ohms and an inductance of 2H. It is connected to a 20V dc supply. Calculate the final value of the voltage across the inductor.
A. 5 V
B. 10 V
C. 0 V
D. 20 V
Answer: C
At a steady-state, the inductor behaves as a short circuit for dc current so, V = 0
55. An RL network is one which consists of __________
A. Resistor and capacitor in parallel
B. Resistor and capacitor in series
C. Resistor and inductor in parallel
D. Resistor and inductor in series
Answer: D
An R-L network is a network that consists of a resistor that is connected in series to an inductor.
56. If the switch is opened at t = 0, what is the current in the circuit?
A. 0 A
B. 1 A
C. 2 A
D. 3 A
Answer: C
Initially, when the switch was closed, the current in the inductor was 60/30 = 2A.
The current in the inductor doesn’t change suddenly so when the switch is opened, the current in the inductor remains the same i.e. 2A.
57. In an RL series circuit, when the switch is closed and the circuit is complete, what is the response?
A. Response does not vary with time
B. Decays with time
C. Increases with time
D. First increases, then decrease
Answer: B
In an RL series circuit, the response decays with time because according to the equation, there is an exponential decrease in the response.
58. If the switch is closed at t = 0, what is the current in the circuit?
A. 0 A
B. 10 A
C. 20 A
D. 30 A
Answer: A
Initially, when the switch is open, the current in the circuit is 0. As soon as the switch is closed at t = 0+, the inductor acts as an open circuit, hence the current in the circuit is zero. Since the current in the circuit is zero, there is no voltage drop across the resistor and hence the voltage across the inductor is equal to the supply voltage, i.e. 60V.
59. What is the voltage across the inductor at t = 0?
A. 0 V
B. 20 V
C. 60 V
D. 58 V
Answer: C
Initially, when the switch is open, the current in the circuit is 0. As soon as the switch is closed at t = 0+, the inductor acts as an open circuit, hence the current in the circuit is zero. Since the current in the circuit is zero, there is no voltage drop across the resistor and the voltage across the inductor is equal to the supply voltage, which is equal to 60V.
60. What is the expression for current in the given circuit?
A. i = 2(e − 2t)A
B. i = 2(1 − e − 2t)A
C. i = 2(e2t)A
D. i = 2(1+e − 2t)A
