Question

An Uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.

Answer 1

Charge supplied by the battery,

q=CV

Energy supplied by the battery,

E=qV=CV2

Energy stored in the capacitor,

U=21CV2

∴ Energy dissipated across R in the form of heat

=E-u

=1/2cv2= u

Answer 2

Shown, that charge stored in capacitor during charging is same as energy dissipated.

• During charging of capacitor , Charge starts flowing from battery till the capacitor is fully charged b.

i.e. till V (capacitor) = V(battery)

or Q = CV

• let at any time t charge on capacitor is q & potential is V

• Also , Work done by battery to to move charge dq against potential V is

W = CV²/2

which stores as potential energy in capacitor

so, U = CV²/2

i.e. energy stored in capacitor after charging is CV²/2

• U(stored) = 1/2 (CV)(V)

• U(stored) = 1/2(Q)(V)

• U(stored) = QV/2

• Total work done by battery on capacitor will be

W = QV

• U(stored) = QV/2

• Heat wasted = QV - QV/2

• Heat wasted = QV/2

hence proved that during charging heat wasted & energy stored in capacitor are same .