Question

A coil of inductance 300mH and resistance 2Ω is connected to a source of voltage 2V. The current reaches half of its steady state value in

• A. 0.1s
• B. 0.05s
• C. 0.3s
• D. 0.15s

Hint:

For RL circuits: t₁/2 = τ ln 2 where τ = (L)/(R).

Answer 1

The Correct Option is B

Step 1: Time constant of RL circuit: τ = (L)/(R) = (0.3)/(2) = 0.15s Step 2: Current growth equation: i = I₀ (1 - e⁻t/τ) For half of steady current: (1)/(2) = 1 - e⁻t/τ ⟹ e⁻t/τ = (1)/(2) Step 3: Solve for time: t = τ ln 2 = 0.15 × 0.693 ≈ 0.05s