Four identical plates each of area $a$ are separated by a distance $d$. The connection is shown below. what…

Four identical plates each of area $a$ are separated by a distance $d$. The connection is shown below. what is the capacitance between $P$ and $Q ?$

1. $2 a \varepsilon_{0} / d$
2. $a \varepsilon_{0} /(2 d)$
3. $a \varepsilon_{0} / d$
4. $4 a \varepsilon_{0} / d$

Solution

Suppose the pair of plates is connected to positive terminal of the battery and the pair of plates $Q$ is connected to the negative terminal of the battery. From figure, it is clear that we have two capacitors $C_{1}$ and $C_{2}$. Positive plates of $C_{1}$ are connected to positive plate of $C_{2}$ and negative plate to negative. Therefore $C_{1}$ and $C_{2}$ are in parallel. So, $\quad C_{p}=C_{1}+C_{2}=2 C=\frac{2 \varepsilon_{0} a}{d}$

Asked in: TEST SERIES MHT-CET Full Test 6

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