Chapter 25: Q29P (page 742)

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

Short Answer

Expert verified

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:

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

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

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

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

$C = \frac{(2) (3.6 \times 10^{7} J)}{{(1000 V)}^{2}} = \frac{7.2 \times 10^{7} J}{10^{6} {(V)}^{2}} = 72 F$

Hence, the value of the capacitance is 72 F.

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

Short Answer

Step by step solution

The given data

Understanding the concept of the energy stored in the capacitor

Calculation of the value of capacitance

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