# Charging a Capacitor

The voltage is gradually increased across the capacitor during charging. Let us consider the rate of increase of voltage across the capacitor is dv/dt at any instant t. The current though the capacitor at that instant is Applying, Kirchhoff’s Voltage Law, in the circuit at that instant, we can write, Integrating both side we get, Now, at the time of switching on the circuit, voltage across the capacitor was zero. That means, v = 0 at t = 0. Putting these values in above equation, we get After getting the value of A, we can rewrite the above equation as, Now, we know that, This is the expression of charging current I, during process of charging. The current and voltage of the capacitor during charging is shown below.

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