In an LCR circuit, charge amplitude decays as Q(t) = Q₀ exp(-Rt/(2L)). Given L = 12 mH and R = 1.5 Ω, calculate the time for the amplitude to decrease to 0.5Q₀.
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Question

In an LCR circuit, charge amplitude decays as Q(t) = Q₀ exp(−Rt/(2L)). Given L = 12 mH and R = 1.5 Ω, calculate the time for the amplitude to decrease to 0.5Q₀.

G1 Physics · Accepted Answer

Step 1: The envelope of damped charge oscillations is Q(t) = Q₀ exp(−Rt/(2L)). Step 2: To reach Q(t) = Q₀/2, solve 1/2 = exp(−Rt/(2L)). Step 3: Taking natural logarithms, t = (2L/R)ln2. Step 4: L = 12 mH = 0.012 H, R = 1.5 Ω; hence t = (2 × 0.012/1.5) × 0.6931 ≈ 0.01109 s. Final answer: (B) 11.09 ms.