Calculate the ratio of the capacitance of two capacitors filled with dielectrics of the same dimensions but of different values K and K 4 arranged in two ways as shown in figure (i) and (ii)

Step-by-step solution

Here, C 1 = ε 0 K 1 A 2 d + ε 0 K 2 A 2 d = ε 0 KA 2 d + ε 0 KA 8 d Given : K 1 = K and K 2 = K 4 = ε 0 KA d 1 2 + 1 8 = ε 0 KA d 4 + 1 8 = 5 ε 0 KA 8 d ...... (i) and C 2 = ε 0 A d 2 K 1 + d 2 K 2 = ε 0 A d 2 K + d 2 K 4 = 2 K ε 0 A 5 d .... (ii) Dividing eqs. (i) by (ii) C 1 C 2 = 5 ε 0 KA 8 d 2 K ε 0 A 5 d = 5 × 5 2 × 8 = 2 5 1 6