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  4. A gang capacitor is formed by interlocking nine plates with each other. The distance between the consecutive plates is 0.885 cm and the overlapping area of the plate is 5 cm 2. The capacity of the unit is

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Q. A gang capacitor is formed by interlocking nine plates with each other. The distance between the consecutive plates is $0.885\, cm$ and the overlapping area of the plate is $5\, cm ^{2}$. The capacity of the unit is

Electrostatic Potential and Capacitance

Solution:

According to the question, the given arrangement of nine plates is equivalent to the parallel combination of $8$ capacitors. The capacity of each capacitor,
$C=\frac{\varepsilon_{0} A}{d}=\frac{8.854 \times 10^{-12} \times 5 \times 10^{-4}}{0.885 \times 10^{-2}}$
$=0.5\, pF$
Hence, the capacity of $8$ capacitors $=8 C=8 \times 0.5=4\, pF$