91Ó°ÊÓ

A capacitor is a charge and energy storage device. The stored energy is proportional to the square of the potential difference between the plates.

The expression for stored energy in the capacitor is given as:

\({\rm{PE}} = \frac{1}{2}C{V^2}\) … (i)

Here, C is the capacitance and V is the potential difference.

The potential difference across the capacitor is,\(V = 5.0\;{\rm{kV}} = 5.0 \times {10^3}\;{\rm{V}}\).

The stored energy in the capacitor is, \({\rm{PE}} = 1200\;{\rm{J}}\).

From equation (i), the capacitance is given as:

\(\begin{aligned}{c}{\rm{PE}} &= \frac{1}{2}C{V^2}\\C &= \frac{{2\left( {{\rm{PE}}} \right)}}{{{V^2}}}\end{aligned}\)

Substitute the values in the above expression.

\(\begin{aligned}{c}C &= \frac{{2 \times \left( {1200\;J} \right)}}{{{{\left( {5.0 \times {{10}^3}\;{\rm{V}}} \right)}^2}}}\\C &= 9.6 \times {10^{ - 5}}\;{\rm{F}}\end{aligned}\)

Thus, the capacitance of the capacitor is \(9.6 \times {10^{ - 5}}\;{\rm{F}}\).