Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates)

Question

Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates) (A)  (1/2)C2V2  (B)  (q2/4 C)  (C)  (1/2)ϵ0( (V/d) )  (D)  (1/2)ϵ0( (V2/d2) )

Tardigrade Admin · Accepted Answer

Energy stored in capacitor of capacitance

C = \frac{1}{2} C V^{2}

Capacitance of a parallel plate capacitor

= C = \frac{A ϵ _{0}}{d}

Volume of parallel plate capacitor

= A d

Thus energy stored per unit volume

= \frac{\frac{1}{2} C V ^{2}}{A d}

= \frac{1}{2} ϵ_{0} \frac{V ^{2}}{d ^{2}}

Q. Energy stored per unit volume of a parallel plate capacitor having plate area $A$ and plate separation d when charged to a potential of $V$ volts is (air space in between the plates)

$\frac{1}{2} C^{2} V^{2}$

$\frac{q ^{2}}{4 C}$

$\frac{1}{2} ϵ_{0} (\frac{V}{d})$

$\frac{1}{2} ϵ_{0} (\frac{V ^{2}}{d ^{2}})$

Energy stored in capacitor of capacitance $C = \frac{1}{2} C V^{2}$
Capacitance of a parallel plate capacitor $= C = \frac{A ϵ _{0}}{d}$
Volume of parallel plate capacitor $= A d$
Thus energy stored per unit volume $= \frac{\frac{1}{2} C V ^{2}}{A d}$
$= \frac{1}{2} ϵ_{0} \frac{V ^{2}}{d ^{2}}$

Q. Energy stored per unit volume of a parallel plate capacitor having plate area A and plate separation d when charged to a potential of V volts is (air space in between the plates)

21​C2V2

4Cq2​

21​ϵ0​(dV​)

21​ϵ0​(d2V2​)