(C) The potential difference across a discharging capacitor is given by $V(t) = V_0 e^{-t/RC}$.Given that at $t = 1 \, \text{s}$, $V(1) = V/3$, we hav

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(C) The potential difference across a discharging capacitor is given by $V(t) = V_0 e^{-t/RC}$.Given that at $t = 1 \, \text{s}$, $V(1) = V/3$, we have:$V/3 = V e^{-1/RC} \implies e^{-1/RC} = 1/3$.We need to find the potential difference at $t = 2 \, \text{s}$:$V(2) = V e^{-2/RC} = V (e^{-1/RC})^2$.Substituting the value of $e^{-1/RC}$:$V(2) = V (1/3)^2 = V/9$.

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

Medium

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

A
$V/3$
B
$V/6$
C
$V/9$
D
$2V/3$

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Class 12 Questions

Class 12

Physics Questions

Chapter

Electrostatic Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

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?

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Find the charge on the capacitor $C$ in the following circuit in $\mu C$.

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$A$ capacitor of capacitance $C = 10 \, \mu F$ is connected to a battery of emf $\varepsilon = 2 \, V$ through a resistor $R$. It is observed that it takes $t = 50 \, ms$ for the charge on the capacitor to reach $q = 12.6 \, \mu C$. Calculate the resistance $R$ of the circuit in $k \Omega$. (Take $1/e \approx 0.37$)

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The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Identify the correct statement$(s)$ related to the $R_1, R_2, C_1$ and $C_2$ of the two $RC$ circuits.

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The electric field between the two parallel plates of a capacitor of $1.5 \mu F$ capacitance drops to one third of its initial value in $6.6 \mu s$ when the plates are connected by a thin wire. The resistance of this wire is . . . . . . . $\Omega$. (Given,$\log_{e} 3 = 1.1$)

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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?

Find the charge on the capacitor $C$ in the following circuit in $\mu C$.

The charge across the capacitor in two different $RC$ circuits $1$ and $2$ are plotted as shown in the figure. Identify the correct statement$(s)$ related to the $R_1, R_2, C_1$ and $C_2$ of the two $RC$ circuits.

The electric field between the two parallel plates of a capacitor of $1.5 \mu F$ capacitance drops to one third of its initial value in $6.6 \mu s$ when the plates are connected by a thin wire. The resistance of this wire is . . . . . . . $\Omega$. (Given,$\log_{e} 3 = 1.1$)

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