First slide

Capacitance

Question

You are given thirty two capacitors each having capacity 4 $μ$ F. How do you connect all of them to prepare a composite capacity having capacitance 8 $μ$ F?

Moderate

A

2 condensers in series and 16 such groups in parallel
B

8 condensers in series and 4 such groups in parallel
C

4 condensers in series and 8 such groups in parallel
D

all of them in series

Solution

Let m condensers are joined in series and n such groups are in parallel.
Capacity of m condensers connected in series
$\frac{1}{C^{'}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \dots = \frac{m}{C} or C^{'} = \frac{C}{m} = \frac{4}{m}$
When n such groups are connected in parallel, then
$C_{eff} = {nC}^{'} = \frac{4 n}{m}$
Given that $G_{eff} = 8, ∴ 8 = \frac{4 n}{m}$
Or $\frac{n}{m} = 2 or n = 2 m . . . (1)$
Further $mn = 32 . . . . (2)$
Now $m \times 2 m = 32 or m = 4$
and n = 2 x 4 = 8

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