First slide

Capacitance

Question

The effective capacitance between points X and Y shown in fig. assuming C₂ = 10 $μ$ F and that the other capacitors are all 4.00 $μ$ F is

Moderate

A

$8 μF$
B

$6 μF$
C

$2.5 μF$
D

$4 μF$

Solution

The equivalent circuit is shown in fig. If a battery is connected between X and Y, the points P and Q are at the same potential because
$C_{1} = C_{4} = C_{3} = C_{5} = 4 μF$
Hence no charge flows through C_2. Now C₁ and C₅ are in series. Hence $\frac{1}{C^{'}} = \frac{1}{C_{1}} + \frac{1}{C_{5}}$
or $C^{'} = \frac{C_{1} C_{5}}{C_{1} + C_{5}} = \frac{4 \times 4}{4 + 4} = 2 μF$
Similarly, C₄ and C₃ are in series and their equivalent capacitance C" is also 2 $μ$ F. Further, C' and C" are in parallel. Hence net capacitance between X and $Y = C^{'} + C^{''} = 2 μF + 2 μF = 4 μF$

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