Calculating the voltage across a capacitor

Calculating the voltage across a capacitor.

The voltage, V, across a capacitor can be expressed as:


A 1.25F capacitor that has an initial voltage of 25.o V is charged with a current that varies with time as i = t (t2 + 6.83)1/2. Find the voltage across the capacitor at 1.00seconds.

Write the initial equation.


Now do the substitution for u, du, n.

   u = t2 + 6.83        du = 2t dt        n = 1/2


Now integrate:

   V = .8* 2/3u2/3 +C = 0.267(t2 + 6.83)2/3+ C

   To solve for the constant, C, we need a set of initial conditions.