How to Calculate the Voltage Across a Capacitor

Formula for Calculating Current through Capacitor

To calculate the voltage across a capacitor, the formula is:

Formula for calculating voltage across a capacitor

All you must know to solve for the voltage across a capacitor is C, the capacitance of the capacitor which is expressed in units, Farads, and the integral of the current going through the capacitor.

Note:V0 is the initial voltage across the capacitor, if any.

Example
If the current going through a capacitor is 10cos(1000t) and its capacitance is 5μF, then what is the voltage across the capacitor?
(*Initial Conditions: The capactior has 0 volts across it initially)

Example of calculating voltage across a capacitor

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