Question

Derive an expression for energy stored in a capacitor. Show that whenever two conductors share charges by bringing them into electical contact , there is a loss of enery.

Answer 1

Let C be the capacitance, V be the voltage and Q be the charge of the capacitor

hence,

Q = CV

we know that work done is defined as the product of voltage and charge

for a small charge dq the energy of he system

dU = V x dq

=> dU = Q/C x dq

integrating both sides we get,

U = Q²/2C

using the eqn Q = CV in the above eqn can be written as,

U = Q²/2C = CV²/2 = QV/2

which are the required expression for energy stored in a capacitor.

when two conductors come in contact with each other, spark is generated which causes the loss of energy.