First slide

Capacitance

Question

To form a composite $16 μ F, 1000 V$ capacitor from a supply of identical capacitors marked $8 μ F, 250 V$ , we require a minimum number of capacitors

Moderate

A

40
B

32
C

8
D

2

Solution

Suppose C = 8 $μ$ F , C' = 16 $μ$ F
and V = 250 V, V' = 1000V

Suppose m rows of given capacitors are connected in parallel and each row contains n capacitors then potential difference across each capacitor $V = \frac{V'}{n}$ and equivalent capacitance of network $C' = \frac{m C}{n}$ on putting the values we get n = 4 and m = 8
$∴$ Total capacitors $= n \times m = 4 \times 8 = 32$

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