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In the circuit shown, the switch S is open for a long time and is closed at t=0. The current i(t) for t≥ 0⁺ is

1. i(t)=0.5-0.125e^(-1000t) A
2. i(t)=1.5-0.125e^(-1000t) A
3. i(t)=0.5-0.5e^(-1000t) A
4. i(t)=0.375e^(-1000t) A

Correct answer: i(t)=0.5-0.125e^(-1000t) A

Solution

The correct option reflects the behavior of the circuit after the switch is closed, where the steady-state current approaches 0.5 A and the transient response decays exponentially with a time constant determined by the circuit components, specifically matching the derived equation for the current.

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