Discharging a Capacitor (Formula And Graphs)

What is Discharging a Capacitor?

Discharging a capacitor means releasing the charge stored within the capacitor. Let’s go over an example where a capacitor is discharged.

We connect a charged capacitor of capacitance C farad in series with a resistor of resistance R ohms.

We then short circuit this series combination by switching on the push switch as shown.
discharging a capacitor
As soon as the capacitor is short-circuited, it starts discharging.

Let us assume, the voltage of the capacitor at fully charged condition is V volt. As soon as the capacitor is short-circuited, the discharging current of the circuit would be – V / R ampere.

But after the instant of switching on that is at t = +0, the current through the circuit is

As per Kirchhoff’s Voltage Law, we get,

Integrating both sides, we get,

Where, A is the constant of integration and, at t = 0, v = V,

After calculating the value of A, we get,

We know the form, KVL of the circuit,

If we plot these discharging current and voltage in the graph, we get,
discharging a capacitor
Hence the capacitor current exponentially reaches zero from its initial value, and the capacitor voltage reaches exponentially to zero from its initial value during discharging.

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