Initial and Final Values of Current in an RLC Circuit

Initial Conditions:
When a series RLC circuit is switched ON to a step voltage V at t=0, the initial conditions for the circuit can be analyzed as follows:

1. Inductor (L):
At t=0, the current flowing through the inductor is zero. This is because the inductor opposes the sudden change in current and takes some time to build up its magnetic field. Hence, the initial current in the inductor is zero.

2. Capacitor (C):
At t=0, the voltage across the capacitor is zero. This is because the capacitor initially acts as a short circuit and charges up slowly over time. Therefore, the initial voltage across the capacitor is zero.

3. Resistor (R):
At t=0, there are no changes in the resistor. The voltage across the resistor is equal to the step voltage V, and the current flowing through the resistor is determined by Ohm's law.

Final Conditions:
The final conditions for the circuit can be analyzed as follows:

1. Inductor (L):
In the steady state, the inductor behaves like a short circuit to DC current. Therefore, when the circuit reaches its final state, the inductor current is zero.

2. Capacitor (C):
In the steady state, the capacitor behaves like an open circuit to DC current. Therefore, when the circuit reaches its final state, the voltage across the capacitor is zero.

3. Resistor (R):
In the steady state, the resistor remains unchanged. The voltage across the resistor is equal to the step voltage V, and the current flowing through the resistor is determined by Ohm's law.

Correct Answer:
The correct answer is option 'C' - zero, zero. This is because in the initial state, the current in the circuit is zero for both the inductor and the capacitor. In the final state, the current in the inductor and the voltage across the capacitor become zero in the steady state. The only component in the circuit that carries current in the final state is the resistor.

To summarize:
- Initial current in the inductor = zero
- Initial voltage across the capacitor = zero
- Final current in the inductor = zero
- Final voltage across the capacitor = zero
- Initial current in the circuit = zero
- Final current in the circuit = zero
- Initial voltage across the resistor = V
- Final voltage across the resistor = V

Hence, the initial and final values of the current in the circuit are both zero.