(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

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Electric Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

At time $t=0$,a battery of $10 \ V$ is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially,at what time (in seconds) does the voltage across them become $4 \ V$? [Take $\ln 5=1.6, \ln 3=1.1$]

IIT 2010

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In the given figure,initially the capacitor is uncharged. The ratio of current at $t = 0$ and $t = \infty$ will be:

Medium

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In a $RC$ circuit, where $R$ is resistance and $C$ is capacitance, which of the following has the dimension of time?

EasyTS EAMCET 2022

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Assertion : $A$ capacitor blocks direct current in the steady state.
Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.

EasyAIIMS 2011

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$A$ resistor $R$ and a $2 \ \mu F$ capacitor in series are connected through a switch to a $200 \ V$ direct supply. Across the capacitor is a neon bulb that lights up at $120 \ V$. Calculate the value of $R$ to make the bulb light up $5 \ s$ after the switch has been closed. (Given: $\log_{10} 2.5 = 0.4$)

MediumAIEEE 2011

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At time $t=0$,a battery of $10 \ V$ is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially,at what time (in seconds) does the voltage across them become $4 \ V$? [Take $\ln 5=1.6, \ln 3=1.1$]

In the given figure,initially the capacitor is uncharged. The ratio of current at $t = 0$ and $t = \infty$ will be:

In a $RC$ circuit, where $R$ is resistance and $C$ is capacitance, which of the following has the dimension of time?

Assertion : $A$ capacitor blocks direct current in the steady state.Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.

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Assertion : $A$ capacitor blocks direct current in the steady state.
Reason : The capacitive reactance of the capacitor is inversely proportional to frequency $f$ of the source of $emf$.