Question

In the textbook, it was shown that the energy stored in a capacitor C charged to a potential V is U=12QV.

Express this energy in terms of the variables Q and C.

Express this energy in terms of the variables C and V.

Answer 1

Energy Stored in capacitor

U=(1/2)QV

since Voltage across capcitor is

V=Q/C

U=(1/2)(Q*Q/C)

U=(1/2)(Q²/C)

b)

Charge

Q=CV

Energy stored in capacitor

U=(1/2)(CV)*V

U=(1/2)CV²

Answer 2

given   U   = QV/2 ---------------1

use the eqn of charge Q as   Q = CV ( from definiton)

we get

in terms of Q and C

eliminate V from 1 ( for this use V = Q/C)

so U = Q * Q/C*2

so U = Q^2/2C ----------------<<<<<<<<<<<<<<<-answer to p;art A

---------------------------

in terms of A C and V , eliminate Q

U = CV * V/2

U = CV^2/C --------------<<<<<<<<<<<<<,answer to part B