A capacitor is charged by a battery. The battery is removed and another identical uncharged capacitor is connected in parallel. The total electrostatic energy of resulting system

Concept:

Capacitor is defined as a component in an electrical circuit which has the ability to store energy in the form of an electrical charge producing a potential difference across its plates. It is like rechargeable battery.

Charge on capacitor is given by:

q = CV

where q is charge stored , V is potential difference across its plates, C is the capacitance of the capacitor.

Energy stored in capacitor is calculated using the formula, U:

\(\rm U= \frac{1}{2}C V^2\)

where q is charge stored , V is potential difference across its plates, C is the capacitance of the capacitor.

Calculation:

Charge on capacitor

q = CV

When it is connected with another uncharged capacitor

 \(V_c =\frac{q_1+q_2}{C_1 + C_2}= \frac{q + 0}{C + C}\)

\(\rm V_c= \frac{V}{2}\)

Initial energy

\(\rm U_f = \frac{1}{2}C \left(\frac{V}{2}\right)^2 + \)\(\rm\frac{1}{2}C\left(\frac{V}{2}\right)^2\)

\(= \rm\frac{CV^2}{4}\)

Loss of energy  = U_i - U_f

_{\(\rm=\frac{CV^2}{4}\)}

i.e. decreases by a factor (2)