Fig. shows two parallel plate capacitors X and Y having same area of plates and same separation between them : X has air while Y has dielectric of constant 4 as medium between plates

(a) calculate capacitance of each capacitor, if equivalent capacitance of combination is ` 4 mu F ` (b) calculate potential difference between plate X and Y (c) what is the ratio of electrostatic energy stored in X & Y.

Answer

(a) ` 5 mu F, 20 muF` (b) ` 9.6 V, 2.4 V` (c )`4 `

Explanation

` C _ x = C, C_y = KC = 4C `
` (C_x C_y)/(C_x + C_y) = (4)/(5) C = 4 rArr C = 5muf `
(a) ` Ceq = C_x = 5 muf `
` C_y = 20 muf `
(b) ` V+ (V)/(4) = 12 (V_x = V, V_y = (V)/(4) ` as q constant )
` V= 9.6 ` Volt, ` V_x = 9.6 ` Volt, ` V_y = 2.4 ` Volt.
(c ) ` (U_x)/(U_y) = ((1)/(2) C_x V_ (x^2))/((1)/(2) C_y(V_y)^2) = 4 `