(B) The potential difference across a discharging capacitor is given by $V(t) = V_0 e^{-\lambda t}$.Given $V_0 = 320 \, V$.After $t = 1 \, s$,$V_1 = 2

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(B) The potential difference across a discharging capacitor is given by $V(t) = V_0 e^{-\lambda t}$.Given $V_0 = 320 \, V$.After $t = 1 \, s$,$V_1 = 240 \, V$.So,$240 = 320 e^{-\lambda} \implies e^{-\lambda} = \frac{240}{320} = \frac{3}{4}$.After $t = 2 \, s$,the potential difference is $V_2 = V_0 (e^{-\lambda})^2 = 320 \times (\frac{3}{4})^2 = 320 \times \frac{9}{16} = 180 \, V$.After $t = 3 \, s$,the potential difference is $V_3 = V_0 (e^{-\lambda})^3 = 320 \times (\frac{3}{4})^3 = 320 \times \frac{27}{64} = 135 \, V$.

Class 12 Physics Electric Potential and Capacitance Charging and Discharging of Capacitance and RC circuit (DC)

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The plates of a capacitor are charged to a potential difference of $320 \, V$ and are then connected across a resistor. The potential difference across the capacitor decays exponentially with time. After $1 \, s$ the potential difference between the plates of the capacitor is $240 \, V$,then after $2 \, s$ and $3 \, s$ the potential difference between the plates will be:

A
$200 \, V$ and $180 \, V$
B
$180 \, V$ and $135 \, V$
C
$160 \, V$ and $80 \, V$
D
$140 \, V$ and $20 \, V$

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Class 12 Questions

Class 12

Physics Questions

Chapter

Electric Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

The circuit shown has been connected for a long time. The voltage across the capacitor is ............. $V$.

MediumKVPY 2013

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In the following circuit,the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$

DifficultJEE MAIN 2018

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At time $t = 0$,the switch $K$ is closed. Which of the following statements is true for the current '$i$' flowing through the resistor $AB$ in the given circuit?

Medium

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$A$ capacitor of capacitance $C = 1 \, \mu F$ is suddenly connected to a battery of $100 \, V$ through a resistance $R = 100 \, \Omega$. The time taken for the capacitor to be charged to $50 \, V$ is $.... \times 10^{-4} \, s$. (Take $\ln 2 = 0.69$)

MediumJEE MAIN 2021

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$A$ light bulb,a capacitor,and a battery are connected in a series circuit as shown in the figure,with switch $S$ initially open. When the switch $S$ is closed,which one of the following is true?

Medium

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The circuit shown has been connected for a long time. The voltage across the capacitor is ............. $V$.

In the following circuit,the switch $S$ is closed at $t = 0.$ The charge on the capacitor $C_1$ as a function of time will be given by $\left( {{C_{eq}} = \frac{{{C_1}{C_2}}}{{{C_1} + {C_2}}}} \right).$

At time $t = 0$,the switch $K$ is closed. Which of the following statements is true for the current '$i$' flowing through the resistor $AB$ in the given circuit?

$A$ capacitor of capacitance $C = 1 \, \mu F$ is suddenly connected to a battery of $100 \, V$ through a resistance $R = 100 \, \Omega$. The time taken for the capacitor to be charged to $50 \, V$ is $.... \times 10^{-4} \, s$. (Take $\ln 2 = 0.69$)

$A$ light bulb,a capacitor,and a battery are connected in a series circuit as shown in the figure,with switch $S$ initially open. When the switch $S$ is closed,which one of the following is true?

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