Question

What capacitance is required to store energy of 10 kW.hat a potential difference of1000V?

Short answer

The capacitance required to store energy of 10 kW.h is 72 F.

Step-by-step solution

The given data

a) The potential difference,V=1000 V .

b) Energy is stored in the capacitor, U =10 kW.h.

Understanding the concept of the energy stored in the capacitor

We use the relation of energy stored in the capacitor to find the capacitance C of the capacitor. We need to convert the given energy into joules.

Formula:

The energy stored by the capacitor is given by, $U=\frac{1}{2}C{V}^2$ (i)

Calculation of the value of capacitance

The equation of the capacitance can be calculated using the given values in equation (i) as follows:

$C=\frac{2U}{V^2}$

Let’s convert the given value of energy in joules as:

$$\begin{gathered} U=10\mathrm{kW}.\mathrm{h}\times \frac{{10}^3\mathrm{W}}{1\mathrm{kW}}\times \frac{3600\mathrm{s}}{1\mathrm{h}} \\ =10\times {10}^3\times 3.6\times {10}^{3}W.s \\ =3.6\times {10}^7\mathrm{W}.\mathrm{s} \\ =3.6\times {10}^7\mathrm{J} \end{gathered}$$

Substituting all values in (a), we get the value of capacitance as:

$$\begin{gathered} \mathrm{C}=\frac{\left(2\right)\left(3.6\times {10}^7\mathrm{J}\right)}{{\left(1000\mathrm{V}\right)}^2} \\ =\frac{7.2\times {10}^7\mathrm{J}}{{10}^6{\left(\mathrm{V}\right)}^2} \\ =72\mathrm{F} \end{gathered}$$

Hence, the value of the capacitance is 72 F.