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Relation between voltage and current

The following equation can be used for any current i(t):

It clearly shows the 90 degrees phase shift if i(t) is sinusoidal: the integral of a sine is a (-)cosine. We also see that, if we charge a capacitor with a constant current I, the voltage across it will increase linearly: v(t) = v(0) + (1/C)∙I∙t.