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  • (a) Derive an expression for the energy stored in a parallel plate capacitor of capacitance C when charged up to voltage V. How is this energy stored in the capacitor ? (b) A capacitor of capacitance

(a) Derive an expression for the energy stored in a parallel plate capacitor of capacitance C when charged up to voltage V. How is this energy stored in the capacitor ?

(b) A capacitor of capacitance 1 \mu F is charged by connecting a battery of negligible internal resistance and emf 10 V across it. Calculate the amount of charge supplied by the battery in charging the capacitor fully.

 

 
 
 
 
 

Answers (1)

a) 

Let the charge on the capacitor is increased by dq amount then,

Then, the work done:-

dU=Vd{Q}'=\frac{{Q}'}{C}\; d{Q}'

On integrating it, we have

\int_{O}^{U}dU=\frac{1}{C}\int_{O}^{Q}{Q}'d\;{Q}'

U=\frac{1}{2}\left [ \frac{Q^{2}}{C} \right ]^{Q}_{O}

U=\frac{1}{2}\frac{Q^{2}}{C}

We know, C=\frac{Q}{V}

            U=\frac{1}{2}CV^{2}

            U=\frac{1}{2}QV

\therefore This is the work done is stored as energy on the capacitor 

The electrostatic Energy energy is stored in the electric field between the plates.

b)

\\Q=CV\\Q=1\times10^{-6}\times10=10\mu C

Posted by

Safeer PP

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