Please make sure the answer is neat so I can read it. James has built a capacito
ID: 1846996 • Letter: P
Question
Please make sure the answer is neat so I can read it.
James has built a capacitor of width W, length L, plate distanced, and has filled it with a dielectric material having a relative dielectric constant Assume L >> d&W;>>d. The maximum voltage that James can apply to this capacitor is limited by Vmax = kd, where K is the breakdown strength of the dielectric. Derive an expression for the maximum energy that can be stored in this capacitor in terms of K & the volume of the dielectric. If James wants to store the maximum energy per unit volume, do the values of L, W&d; matter? If yes, explain how they matter. If no, then explain which parameters matter?Explanation / Answer
Area A = WL
C = ?0*?r*A/d = ?0*?r*WL/d
Vmax = kd
E = (1/2)*C*Vmax^2
= (1/2)*(?0*?r*WL/d)*(kd)^2 = (1/2)*(?0*?r*WL/d)*k^2d^2
E = (1/2)*(?0*?r*WL)k^2*d
E = (1/2)*(?0*?r*k^2)*(WLd)
volume of dielectirc V= WLd
(i) E=(1/2)*?0*?r*k^2*V
(ii) per unit volume
(E/V) = (1/2)*?0*?r*k^2
no it does not depends on L,W,d
It depends on ?r & k.