(D) The potential difference across a discharging capacitor is given by $V = V_0 e^{-t/CR}$.Given $V_0 = 50 \, V$ and $V = 40 \, V$ at $t = 1 \, s$,we

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(D) The potential difference across a discharging capacitor is given by $V = V_0 e^{-t/CR}$.Given $V_0 = 50 \, V$ and $V = 40 \, V$ at $t = 1 \, s$,we have $40 = 50 e^{-1/CR}$,which implies $e^{-1/CR} = 4/5$.For option $(b)$,the potential difference after $t = 2 \, s$ is $V' = V_0 e^{-2/CR} = 50 (e^{-1/CR})^2 = 50 (4/5)^2 = 50 \times (16/25) = 32 \, V$. Thus,$(b)$ is correct.For option $(a)$,the energy stored in a capacitor is $U = \frac{1}{2} C V^2$. The fraction of energy remaining after $1 \, s$ is $U_f / U_i = (V_f / V_i)^2 = (40/50)^2 = (4/5)^2 = 16/25$. Thus,$(a)$ is correct.Since both $(a)$ and $(b)$ are correct,the correct option is $(d)$.

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

Medium

$A$ parallel plate capacitor is charged to a potential difference of $50 \, V$. It is discharged through a resistance. After $1 \, s$,the potential difference between the plates becomes $40 \, V$. Then:

A
Fraction of stored energy after $1 \, s$ is $16/25$.
B
Potential difference between the plates after $2 \, s$ will be $32 \, V$.
C
Potential difference between the plates after $2 \, s$ will be $20 \, V$.
D
Both $(a)$ and $(b)$.

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Electric Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

For the $RC$ circuit shown,the resistance is $R = 10.0\ \Omega$,the capacitance is $C = 5.0\ F$ and the battery has voltage $\xi = 12\ V$. The capacitor is initially uncharged when the switch $S$ is closed at time $t = 0$. At some time later,the current in the circuit is $0.50\ A$. What is the magnitude of the charge across the capacitor at that moment (in $C$)?

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EasyWBJEE 2019

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The plates of a capacitor are charged to a potential difference of $V \, \text{volts}$ and then connected across a resistor. The potential difference across the capacitor decreases exponentially with respect to time. After one second, the potential difference between the plates is $V/3$; then after two seconds from the start, the potential difference between the plates is

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$A$ parallel plate capacitor is charged to a potential difference of $50 \, V$. It is discharged through a resistance. After $1 \, s$,the potential difference between the plates becomes $40 \, V$. Then:

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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?

$A$ $4\,\mu F$ capacitor is charged to $400\,V$ and then its plates are joined through a resistance of $1\,k\Omega$. The heat produced in the resistance is ............... $J$.

$A$ capacitor of capacitance $C$ is connected in series with a resistance $R$ and a $DC$ source of $emf$ $E$ through a key. The capacitor starts charging when the key is closed. By the time the capacitor has been fully charged,what amount of energy is dissipated in the resistance $R$?

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