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)

Question

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), 5 : 2, 25 : 16, 5 : 4, 2 : 5

MARKS App · Accepted Answer

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

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