A 4 $\mu F$ capacitor, a resistance of $2.5\ M\Omega$ is in series with $12\ V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given $\ln{(2) = 0.693}$]

Question

Dr. Abubacker · Accepted Answer

(a) During the growth of voltage in a $C - R$ circuit the voltage across a capacitor at time $t$ is given by $V = V_{0}(1 - e^{\frac{t}{CR}})$ for the given circuit as per given conduction at time $t$
$V = \frac{3}{4}$ th of the voltage applied across $C = \frac{3}{4}V_{0}$
So, $\frac{3}{4}V_{0} = V_{0}\left( 1 - e^{\frac{t}{RC}} ight) \Rightarrow e^{\frac{t}{RC}} = \frac{1}{4} \Rightarrow e^{\frac{t}{RC}} = 2^{2}$
$\Rightarrow 2RC\ln 2 = 2 	imes (2.5 	imes 10^{6}) 	imes (4 	imes 10^{- 6}) 	imes (0.693)$
$= 13.86\ s$

Q. A 4 $\mu F$ capacitor, a resistance of $2.5\ M\Omega$ is in series with $12\ V$ battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given $\ln{(2) = 0.693}$]

Explanation

Reviewed by Dr. Abubacker

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