Energy per unit volume for a capacitor having | vedclass

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Question

(D) For a parallel plate capacitor,the capacitance is $C = \frac{A \varepsilon_{0}}{d}$.The volume of the capacitor is $V_{vol} = Ad$.The total energy

Vedclass · Accepted Answer

$\frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}$

Vedclass · Answer

(D) For a parallel plate capacitor,the capacitance is $C = \frac{A \varepsilon_{0}}{d}$.The volume of the capacitor is $V_{vol} = Ad$.The total energy stored in the capacitor is $U = \frac{1}{2} CV^{2}$.The energy per unit volume (energy density) is given by $u = \frac{U}{V_{vol}} = \frac{\frac{1}{2} CV^{2}}{Ad}$.Substituting $C = \frac{A \varepsilon_{0}}{d}$ into the expression:$u = \frac{\frac{1}{2} (\frac{A \varepsilon_{0}}{d}) V^{2}}{Ad} = \frac{1}{2} \varepsilon_{0} \frac{V^{2}}{d^{2}}$.

Energy per unit volume for a capacitor having area $A$ and separation $d$ kept at potential difference $V$ is given by

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