# Basic Electrical Engineering Questions and Answers – Analysis of Growth & Decay

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This set of Basic Electrical Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Analysis of Growth & Decay”.

1. What is the total applied voltage in an inductive circuit?
a) V=Ri+Ldi/dt
b) V=Ri+di/dt
c) V=i+Ldi/dt
d) V=R+Ldi/dt

Explanation: The total voltage in an inductive circuit is the sum of the voltage due to the resistor which is Ri and the voltage due to the inductor which is Ldi/dt. Hence V=Ri+Ldi/dt.

2. What is Helmholtz equation?
a) i=I(eRt/L)
b) i=I(1-e-Rt/L)
c) i=I(1+e-Rt/L)
d) i=I(e-Rt/L)

Explanation: Helmholtz equation is an equation which gives the formula for the growth in an inductive circuit. Hence the Helmholtz formula is: i=I(1-e-Rt/L).

3. 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 current in the circuit.
a) 5A
b) 10A
c) 0 A
d) 20A

Explanation: Initially, inductor behave as open circuit for dc current so, i=0.
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4. 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 current in the circuit.
a) 5A
b) 10A
c) 15A
d) 20A

Explanation: The final value of the current in the circuit is:
I=V/R = 5A.

5. A coil has a resistance of 4 ohms and an inductance of 2H. It is connected to a 20V dc supply. Calculate the value of current 1s after the switch is closed.
a) 5.44A
b) 4.32A
c) 6.56A
d) 2.34A

Explanation: We know that:
i=I(1-eRt/L)
I=V/R=5A
Substituting the remaining values from the given question, we get i=4.32A.
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6. A coil has a resistance of 4 ohms and an inductance of 2H. It is connected to a 20V dc supply. Calculate the value of voltage 1s after the switch is closed.
a) 5.4V
b) 10.8V
c) 0 V
d) 2.7V

Explanation: V=V0e-Rt/L
V=20e-2=2.7V.

7. 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)

Explanation: 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, the voltage also increases.

8. 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

Explanation: We know that: V=V0(e-tR/L).
When t=L/R, we have: V=V0(e-1) = 0.37*Vsub>0.
Hence the time constant is the time taken for the voltage in an inductive circuit to become 0.37 times its initial voltage.

9. 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

Explanation: Initially, inductor behave as open circuit for dc current so, V = V0 = 20V i.e. same as voltage source.

10. 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) 5V
b) 10V
c) 0 V
d) 20V

Explanation: At steady state, inductor behaves as a short circuit for dc current so, V=0

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