Question 680: Electrostatics & Capacitance

Question

A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a) and then in Fig.(b). Then ratio of the capacitor in the two arrangements is

Accepted Answer

In Fig. (a), $$C=\frac{2 \varepsilon_0 \frac{A}{2}}{d}+\frac{3 \varepsilon_0 \frac{A}{2}}{d}=\frac{5 \varepsilon_0 A}{2 d}$$
In Fig. (b),
$$\begin{aligned}
& C^{\prime}=\frac{\left(\frac{3 \varepsilon_0 A}{\frac{d}{2}}ight)\left(\frac{2 \varepsilon_0 A}{\frac{d}{2}}ight)}{\frac{2 \varepsilon_0 A}{\frac{d}{2}}+\frac{3 \varepsilon_0 A}{\frac{d}{2}}} \
& C^{\prime}=\frac{6 \varepsilon_0 A}{\frac{d / 2}{5}}=\frac{12 \varepsilon_0 A}{5 d} \
& \frac{C}{C^{\prime}}=\frac{5 \varepsilon_0 A}{2 d} 	imes \frac{5 d}{12 \varepsilon_0 A}=\frac{25}{24}
\end{aligned}$$

Answer

25 : 24

Answer

24 : 25

Answer

12 : 13

Answer

13 : 12

Electrostatics & Capacitance

A capacitor is filled with two dielectrics of the same dimensions but of dielectric constants 2 and 3 as shown in Fig.(a) and then in Fig.(b). Then ratio of the capacitor in the two arrangements is

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