The amplitude of the charge oscillating in a circuit decreases exponentially as Q = Q 0 e − Rt 2 L , where Q 0 is the charge at t = 0 s . The time at which charge amplitude decreases to 0.50 Q 0

Question

The amplitude of the charge oscillating in a circuit decreases exponentially as Q = Q 0 ​ e − Rt 2 L , where Q 0 ​ is the charge at t = 0 s . The time at which charge amplitude decreases to 0.50 Q 0 ​ is nearly: [Given that R = 1.5Ω , L = 12 mH , ln ( 2 ) = 0.693 ]NEET 2024 (Re-NEET)

TestHub · Accepted Answer

Given Q = Q 0 ​ e − Rt /2 L R = 1.5Ω , L = 12 mH , In ( 2 ) = 0.693 Q = 0.5 Q 0 ​ , t = ? 0.5 Q 0 ​ = Q 0 ​ e − Rt /2 L ⇒ 2 1 ​ = e − Rt /2 L Taking log on both sides ln ( 2 1 ​ ) = ln e − Rt /2 L ⇒ ln 2 = 2 L Rt ​ t = R 2 L In 2 ​ = 1.5 2 × 12 × 1 0 − 3 × 0.693 ​ t = 11.09 ms

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