SOLVED: Help with Art of Electronics exercise: Capacitors

[SpannersToSparks]

Hi

Can anyone help with this exercise in AoE (Third Edition) please? Its page 19-20 of the book (not the student manual).

"When you charge up a capacitor, you're supplying energy. The capacitor doesn't get hot; instead it stores the energy in its internal electric fields. Its an easy exercise [ ] to discover for yourself that the amount of stored energy in a charged capacitor is just

U_c = (1/2)CV²

Where U_c is in joules, C in Farads and V in volts. This is an important result - we will see it often.

Exercise 1.14 - Take the Energy Challenge: Imagine charging up a capacitor of capacitance C, from 0V to some final voltage V_f. If you do it right, the result won't depend on how you get there, so you don't need to assume constant current charging (though you're welcome to do so). At any instant the rate of flow of energy into the capacitor is VI (joules/s); so you need to integrate dU = VI dt from start to finish. Take it from there."

The book keeps telling me that maths is out of keeping with The Art Of Electronics, then stumping me with maths questions

Thanks for reading,

Spanners

[SpannersToSparks]

Ack NVM, I figured it out.

Substitute I = C(dV/dt) in [dU = VI dt] and then integrate.