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A typical RC circuit is as shown in the figure below. It consists of a resistor, capacitor, a battery and a switch.
To analyze this circuit Kirchhoff’s rule for a closed loop is applied. Accordingly, the equation for the closed loop when the capacitor is charging is given by,
Here, q/C is the potential difference across the capacitor and IR is the potential difference across the resistor. At t = 0, the initial current in the circuit is I0 = ε / R. When the capacitor is fully charged to a maximum value Q then the current in the circuit is zero so that the maximum charge would be Q = Cε. Now the charge at any time t would be given as:
Then the current flowing through the circuit at any time would be given by,
When the capacitor is discharging the amount of charge as a function of time is given as:
Accordingly, the current is given as:
where Q/RC = I0 is the initial current. The negative sign indicates that the capacitor is discharging.
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