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← JEE Main 2022 · 29 Jun · Shift 2
PhysicsSingle correct+4 / -1Question 37 of 90

JEE Main 2022 · 29 Jun · Shift 2, Physics question 37

A capacitor is discharging through a resistor R. Consider in time t1t_1, the energy stored in the capacitor reduces to half of its initial value and in time t2t_2, the charge stored reduces to one eighth of its initial value. The ratio t1/t2t_1/t_2 will be

Choose one option
Answer and worked solution

Official answer: D

Energy ∝e−2t/RC\propto e^{-2t/RC}: t1=RCln⁡22t_1=\frac{RC\ln2}2. Charge 18\frac18: t2=3RCln⁡2t_2=3RC\ln2.

Ratio 16\frac16.

(D)