A charged capacitor of capacitance C is discharging through a resistor of resistance R. At what time the charge on the capacitor is equal to one half…

Question

A charged capacitor of capacitance C is discharging through a resistor of resistance R. At what time the charge on the capacitor is equal to one half of its initial value?

MARKS Content Team · Accepted Answer

Correct answer: (C) RClog_(e )2. The charge on the capacitor at time t in a discharging circuit is given by q=q_0e^(-t/τ) where, τ=RC= time constant ∴ q=q_0e^(-t/RC) when, q=q_02 then q_02=q_0e^(-t/RC) 1/2=e^(-t/RC) Taking natural log on both side log_e1/2=log_0e^(-t/RC) -log_e2=-t/RClog_ee ⇒t=RClog_e2

A charged capacitor of capacitance $C$ is discharging through a resistor of resistance $R$ . At what time the charge on the capacitor is equal to one half of its initial value?

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