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Question

In the given circuit, all three capacitor are identical and have capacitance C μF each. Each resistor has resistance R Ω. An ideal cell of emf V volt is connected as shown. If potential difference across capacitor C3 in steady state is (ab)V, then value of a×b is_______:


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Solution

At steady state, no current will flow through capacitors.
Hence, current will not flow through the branches containing capacitors.

Thus effectively there are resistances 3R and 3R connected in parallel with battery V volt.


The potential at point 1 and 2 is same because both the parallel branches are identical.
So, potential difference across both R Ω resistors is same i.e i2R

The potential difference across each R Ω resistance is V=V3

Drawing the equivalent capacitor circuit by assigning zero potential as shown in figure.


Here, ΔV=2V3V3=V3

In series combination of capacitors, potential difference will distribute in inverse ratio of capacitance,

(ΔV)3=(C1+C2)(C1+C2)+C3.ΔV

(ΔV)3=2C3C(V3)

(ΔV)3=23×V3=2V9

On comparing with (ab)V
we get,

a=2 & b=9

a×b=2×9=18

Accepted answer : 18

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