A parallel plate capacitor with air as medium | vedclass

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Question

(C) The initial capacitance of the air-filled capacitor is $C = \frac{\varepsilon_0 A}{d} = 10\,\mu F$.When the area is divided into two equal halves

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(C) The initial capacitance of the air-filled capacitor is $C = \frac{\varepsilon_0 A}{d} = 10\,\mu F$.When the area is divided into two equal halves $(A_1 = A_2 = A/2)$ and filled with dielectrics,the two parts act as capacitors in parallel.The equivalent capacitance $C_{eq}$ is given by $C_{eq} = C_1 + C_2$.Here,$C_1 = \frac{k_1 \varepsilon_0 (A/2)}{d} = k_1 	imes \frac{C}{2} = 2 	imes \frac{10}{2} = 10\,\mu F$.And $C_2 = \frac{k_2 \varepsilon_0 (A/2)}{d} = k_2 	imes \frac{C}{2} = 4 	imes \frac{10}{2} = 20\,\mu F$.Therefore,$C_{eq} = 10 + 20 = 30\,\mu F$.

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