(D) When switch $S_1$ is closed and $S_2$ is open,the circuit behaves as a simple series $RC$ circuit consisting of the battery $V$,resistor $R$,and c

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At $t = 2\tau$,$q = CV(1 - e^{-2})$

(D) When switch $S_1$ is closed and $S_2$ is open,the circuit behaves as a simple series $RC$ circuit consisting of the battery $V$,resistor $R$,and capacitor $C$.The charge $q$ on the capacitor at any time $t$ is given by the charging formula: $q(t) = CV(1 - e^{-t/\tau})$,where $\tau = RC$.Checking option $D$: At $t = 2\tau$,substituting the value into the formula gives $q = CV(1 - e^{-2\tau/\tau}) = CV(1 - e^{-2})$.Thus,option $D$ is the correct statement.

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

Medium

In an $RC$ circuit as shown below,both switches are open initially. Now switch $S_1$ is closed and $S_2$ is kept open. ($q$ is the charge on the capacitor and $\tau = RC$ is the capacitive time constant). Which of the following statements is correct?

JEE MAIN 2013 All JEE MAIN

A
At $t = \frac{\tau}{2}$,$q = CV(1 - e^{-0.5})$
B
Work done by the battery is half of the energy dissipated in the resistor
C
At $t = \tau$,$q = \frac{CV}{2}$
D
At $t = 2\tau$,$q = CV(1 - e^{-2})$

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Class 12

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Chapter

Electric Potential and Capacitance

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Charging and Discharging of Capacitance and RC circuit (DC)

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In an $RC$ circuit as shown below,both switches are open initially. Now switch $S_1$ is closed and $S_2$ is kept open. ($q$ is the charge on the capacitor and $\tau = RC$ is the capacitive time constant). Which of the following statements is correct?

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In the circuit shown in the figure,what happens in the steady state?

During the charging of a capacitor,the variation of the potential $V$ of the capacitor with time $t$ is shown as:

When the switch $K$ is closed at $t = 0$,what can be said about the current passing through the resistor $AB$ in the given circuit?

In the given circuit, the potential difference across the plates of the capacitor $C$ in steady state is (in $V$)

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