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)3/2+ C

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

        When t = 0, V = 25V.

So, 25 = 0.267((0)2 + 6.83)3/2+ C

        C = 20.2 V

Then V = 0.267(t2 + 6.83)2/3+ 20.2.

And when t = 1 sec, V = 26.0V


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