At time t = 0 Switch S is closed in the circuit shown. What is the expression for the current i(t) through the inductor? [Figure description: A 60 V source on the left feeds a top rail. Two vertical branches: left branch has two 20 Ω resistors in series (top and bottom, with a middle node); right branch has a 20 Ω resistor on top in series with a 2 H inductor (current i(t) flowing down) below it. Switch S (closes at t = 0) connects the left branch's middle node to the right branch's middle node (between the 20 Ω resistor and the inductor).]
- A. 6 - (3 × e^(-10t))
- B. 6 - (3 × e^(-10t/3))
- C. 6 - (3 × e^(-5t))
- D. 6 - (3 × e^(-5t/3))
Answer: B. 6 - (3 × e^(-10t/3))
Explanation: Initial current i(0) = 3 A, final steady-state current i(∞) = 6 A, and time constant τ = L/Rth = 2/(20/3) = 0.3 s (1/τ = 10/3), so i(t) = 6 − 3e^(−10t/3) A.