(A) When the capacitor is fully charged, the charge on it is $q = CE$.The total work done by the $DC$ source (battery) is $W = qE = (CE)E = CE^2$.The

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(A) When the capacitor is fully charged, the charge on it is $q = CE$.The total work done by the $DC$ source (battery) is $W = qE = (CE)E = CE^2$.The energy stored in the capacitor is $U = \frac{1}{2} CE^2$.According to the law of conservation of energy, the work done by the battery is equal to the sum of the energy stored in the capacitor and the energy dissipated as heat in the resistor $R$.Therefore, the energy dissipated in the resistance $R$ is given by:$H = W - U$$H = CE^2 - \frac{1}{2} CE^2$$H = \frac{1}{2} CE^2$.

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

Easy

$A$ 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 $R$?

WBJEE 2019 All WBJEE

A
$\frac{1}{2} C E^{2}$
B
$0$
C
$C E^{2}$
D
$\frac{E^{2}}{R}$

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Class 12

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Chapter

Electrostatic Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

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$A$ 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 $R$?

Similar Questions

Given $R_1 = 1\,\Omega$,$C_1 = 2\,\mu F$ and $R_2 = 2\,\Omega$,$C_2 = 4\,\mu F$. The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

When a capacitor is connected to a battery,

In order to obtain a time constant of $10 \ s$ in an $RC$ circuit containing a resistance of $10^3 \ \Omega$,the capacity of a condenser should be..... $\mu F$.

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