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In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A)
Option: 1 \frac{15}{34} \frac{K \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}
Option: 2 \frac{15}{6} \frac{K \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}
Option: 3 \frac{25}{6} \frac{\mathrm{K} \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}
Option: 4 \frac{9}{6} \frac{\mathrm{K} \varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}

Answers (1)

best_answer

For capacitor in series connection,

\begin{aligned} c &=\frac{A \epsilon _{0}}{\frac{t_{1}}{k_{1}}+\frac{t_{2}}{k_{2}}+\frac{t_{3}}{k_{3}}} \\ &=\frac{A \varepsilon_{0}}{\frac{d}{k}+\frac{2 d}{3 k}+\frac{3 d}{5 k}} \end{aligned}

\begin{aligned} &=\frac{A \varepsilon_{0}}{\frac{15 d+10 d+9 d}{15 k}} \\ C_{\text {eq }} &=\frac{15 A \varepsilon_{0} k}{34 d} \end{aligned}

The correct option is (1).

Posted by

vishal kumar

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