First slide

Capacitance

Question

Referring to fig. the effective capacitance between A and B will be

Easy

A

$3 μF$
B

$(36 / 13) μF$
C

$13 μF$
D

$7 μF$

Solution

The upper two condensers of capacities 3 $μ$ F and 6 $μ$ F are in series. Their resultant capacitance C' will be
$\frac{1}{C^{'}} = \frac{1}{3} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} or C^{'} = 2 μF$
Similarly, the lower two condensers of capacities 2 $μ$ F and 2 $μ$ F are in series. Their resultant capacitance C' will be
$\frac{1}{C^{''}} = \frac{1}{2} + \frac{1}{2} = 1 or C^{''} = 1 μF$
The effective capacitance between A and B will be
$C = C^{'} + C^{''} = 2 + 1 = 3 μF$

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