Question

Find the equivalent capacitance of the combination of capacitors between the points A and B as shown in figure.
Also calculate the total charge that flows in the circuit when a 100 V battery is connected between the points
A and B​

Answer 1

The equivalent capacitance of the circuit is 20 μF and the charge flowing through the circuit is 2000 μC.

Given,

The value of capacitance C₁ = 40μF, C₂= 60μF, C₃ = 60μF, C₄ = 60μF, C₅ = 10μF, and C₆ = 10μF.

A battery of 100 V is connected.

To Find,

The equivalent capacitance and the charge flowing in the circuit.

Solution,

The capacitors C₂, C₃, and C₄ are connected in series

Let us assume that their equivalent capacitance is C'

So,

1/C' = 1/60+1/60+1/60

1/C' = 3/60

C' = 20 μF

The capacitors C₅ and C₆ are connected in series

Let us assume that their equivalent capacitance is C".

So,

C" = 10+10 = 20 μF.

Now, C' and C" are connected in parallel

Let us assume that their equivalent capacitance is C'''

C''' = 20+20 = 40 μF

Now, C₁ and C''' are connected in series

So,

1/C = 1/40+1/40

C = 20 μF.

Now,

Q = CV

Q = 20*100 = 2000 μC.

Hence, the equivalent capacitance of the circuit is 20 μF and the charge flowing through the circuit is 2000 μC.

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