11. If the switch is closed at t = 0, what is the current in the circuit?
A. 0A
B. 10A
C. 20A
D. Infinity
Answer: B
As soon as the switch is closed at t = 0, the capacitor acts as a short circuit. The current in the circuit is:
I = V/R = 100/10 = 10A.
12. Calculate the voltage across the capacitor at t = 0.
A. 0V
B. 10V
C. 20V
D. Infinity
Answer: A
When the switch is closed at t = 0, the capacitor has no voltage across it since it has not been charged. The capacitor acts as a short circuit and the voltage across it is zero.
13. Calculate di(0)/dt if the switch is closed at t = 0.
A. -9.9A/s
B. -10A/s
C. 0A/s
D. -0.1A/s
Answer: D
Applying KVL to the given circuit, we get:
i = i0e-t/RC = (100/10)e-t/100
i = 10 e-t/100
di/dt = -(10/100) e-t/100
di(0)/dt = -0.1A/s.
14. Calculate d2i(0)/dt2 from the given circuit.
A. 10-6A/s2
B. 10-3A/s2
C. 106A/s2
D. 103A/s2
Answer: B
Applying KVL to the given circuit, we get:
100+10i(0)+1/10 × ∫(i(0)dt) = 0
Differentiating once, we get:
10di(0)/dt+1/10 × i.
Differentiating once again, we get:
10d2i(0)/dt2+10di(0)/dt = 0.
Substituting the values of di/dt from the previous explanation, we get d2i(0)/dt2 = 10-3A/s2.
15. The current equation for the given circuit is?
A. i = 10e(-0.01)t A
B. i = 10e(0.01)t A
C. i = 10e(-0.001)t A
D. i = 100e(-0.01)t A
Answer: A
The KVL equation is:
100+10i(0)+1/10 × ∫(i(0)dt) = 0
On applying a Laplace transform to this equation, we get:
100/s = I(s)/10s+10I(s)
Solving the equation, we get:
i = 10e(-0.01)t A.
16. The expression for the current in an RC circuit is?
A. i = (V/R)et/RC
B. i = (V/R)e-t/RC
C. i = (V/R)(1-e-t/RC)
D. i = (V/R) (1-et/RC)
Answer: B
Applying KVL to the given circuit, we get:
i = i0e-t/RC = (100/10)e-t/100
i = 10 e-t/100.
17. What is the voltage in the resistor as soon as the switch is closed at t = 0.
A. 0V
B. Infinity
C. 220V
D. Insufficient information provided
Answer: C
As soon as the switch is closed at t = 0, there is no charge in the capacitor, hence the voltage across the capacitor is zero and all the 220V voltage is the voltage across the resistor.
18. Work done in charging a capacitor is ____________
A. QV
B. 1⁄2QV
C. 2QV
D. QV2
Answer: B
We know that work done = Q2/2C.
Substituting C as Q/V, we get work done = Q/2V.
19. Energy stored in a 2000mF capacitor charged to a potential difference of 10V is?
A. 100J
B. 200J
C. 300J
D. 400J
Answer: A
From the expression of Capacitor energy
WD = CV2/2 = 100J.
20. When do we get maximum energy from a set of capacitors?
A. When they are connected in parallel
B. When they are connected in series
C. Both in series and parallel
D. Insufficient information provided
Answer: A
We get maximum energy when capacitors are connected in parallel because the equivalent capacitance is larger than the largest individual capacitance when connected in parallel. The relation between capacitance and energy is:
Energy = CV2/2, hence as the capacitance increases, the energy stored in it also increases.