Topic: Network Theory
The voltage V in the circuit given below is :
- A. 0V
- B. 1 V
- C. 2 V
- D. Infinity
Answer: B. 1 V
Explanation: A unit step input implies $V_{in}(t) = 1$ V for $t \ge 0$. Prior to $t=0$, the circuit is unenergized, so the initial current $i(0^-) = 0$. Because the current through an inductor cannot change instantaneously, the current just after the switch closes is $i(0^+) = i(0^-) = 0$ A. Applying Kirchhoff's Voltage Law (KVL) at $t = 0^+$: $V_{in}(0^+) = i(0^+) R + V_L(0^+)$. Substituting the values: $1 = (0 \times 2) + V_L(0^+)$, which results in $V_L(0^+) = 1$ V.