Physics - Capacitor Question with Solution | TestHub

PhysicsCapacitorR-C CircuitMedium2 minPYQ_2019

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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?

Options:

Answer:

Solution:

The charge on the capacitor at time $t$ in a discharging circuit is given by $q = q_{0} e^{- t / τ}$

where, $τ = R C =$ time constant
$∴$ $q = q_{0} e^{- t / R C}$

when, $q = \frac{q_{0}}{2}$

then $\frac{q_{0}}{2} = q_{0} e^{- t / R C}$

$\frac{1}{2} = e^{- t / R C}$

Taking natural log on both side $\log_{e} (\frac{1}{2}) = \log_{0} e^{- t / R C}$

$- \log_{e} 2 = - \frac{t}{R C} \log_{e} e$

$\Rightarrow t = R C \log_{e} 2$

Stream:BITSATSubject:PhysicsTopic:CapacitorSubtopic:R-C Circuit

⏱ 2mℹ️ Source: PYQ_2019

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