Question

Two capacitors of unknown capacitances are connected in series and parallel. If the net capacitances in the two combinations are 6µF and 25µF respectively, find their capacitances.

Answer 1

Hey.

Here is the answer.

In Parallel Connection :

$c \: eqv \: = \: c1 \: + \: c2 \\ \\ in \: series \: \\ \\ c \: eqv. \: = ( \frac{c1 \times c1}{c1 \: + \: c2} )$

Let c1 and c2 be two capacitors;

Then 25 = c1 + c2

so, c2 = 25 - c1

also,

$6 = ( \frac{c1 \times c2}{c1 + c2}) \\ \\ 6(c1 + c2) = c1.c2 \\ \\ 6 \times 25 = c1.c2 \\ \\ 150 = c1 \times (25 - c1) \\ \\ 150 = 25c1 - {c1 }^{2} \\ \\ {c1}^{2} - 25c1 + 150 = 0 \\ \\ {c1}^{2} - 10c1 - 15c1 + 150 = 0 \\ \\ c1(c1 - 10) - 15(c1 - 10) = 0 \\ \\ (c1 - 10)(c1 - 15) = 0 \\ \\ so \: \: c1 = 10 \: and \: 15. \\ \\ so \: c2 = 25 - 10 = 15 \\ \\ or \: c2 = 25 - 15 = 10 \\ \\ so \: 10 \: and \: 15 microfarad\: \: are \: the \: two \: capacitors.$


Thanks.