1. A CR network is one which consists of _________

A. A capacitor and resistor connected in parallel
B. A capacitor and resistor connected in series
C. A network consisting of a capacitor only
D. A network consisting of a resistor only

Answer: B

A CR network consists of a capacitor connected in series with a resistor. The capacitor discharges or charges through the resistor.

A. Open circuit
B. Short circuit
C. Resistor
D. Inductor

Answer: A

Capacitive Reactance X_{C} = 1/(2πfC).

For DC, f = 0 so, X_{C} becomes infinite.

Hence for dc, the capacitor acts as an open circuit.

3. In an RC 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 RC series circuit, the response decays with time because according to the equation, there is an exponential decrease in the response.

4. 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.

5. 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.

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6. 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 = i_{0}e^{-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.

7. Calculate d^{2}i(0)/dt^{2} from the given circuit.

A. 10^{-6}A/s^{2}
B. 10^{-3}A/s^{2}
C. 10^{6}A/s^{2}
D. 10^{3}A/s^{2}

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:

10d^{2}i(0)/dt^{2}+10di(0)/dt = 0.

Substituting the values of di/dt from the previous explanation, we get d^{2}i(0)/dt^{2} = 10^{-3}A/s^{2}.

8. 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.

9. The expression for the current in an RC circuit is?

A. i = (V/R)e^{t/RC}
B. i = (V/R)e^{-t/RC}
C. i = (V/R)(1-e^{-t/RC})
D. i = (V/R) (1-e^{t/RC})

Answer: B

Applying KVL to the given circuit, we get:

i = i_{0}e^{-t/RC} = (100/10)e^{-t/100}

i = 10 e^{-t/100}.

10. 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.