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:

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