At time t = 0,the switch K is closed. Which o | vedclass

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(A) At $t = 0$,the capacitor acts as a short circuit (resistance $R_C = 0$). The circuit consists of the $2 \ V$ battery and the $1000 \ \Omega$ resis

Vedclass · Accepted Answer

At $t = 0$,$i = 2 \ mA$ and it decreases to $1 \ mA$ as time passes.

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(A) At $t = 0$,the capacitor acts as a short circuit (resistance $R_C = 0$). The circuit consists of the $2 \ V$ battery and the $1000 \ \Omega$ resistor in series with the shorted capacitor branch. Thus,the current $i$ is given by $i = \frac{V}{R} = \frac{2 \ V}{1000 \ \Omega} = 2 \ mA$.As $t 	o \infty$,the capacitor becomes fully charged and acts as an open circuit (resistance $R_C = \infty$). The current now flows through both $1000 \ \Omega$ resistors in series. The total resistance is $R_{total} = 1000 \ \Omega + 1000 \ \Omega = 2000 \ \Omega$. Thus,the steady-state current is $i = \frac{V}{R_{total}} = \frac{2 \ V}{2000 \ \Omega} = 1 \ mA$.Therefore,at $t = 0$,$i = 2 \ mA$,and as time passes,the current decreases exponentially to $1 \ mA$.

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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