The correct option is
B 18At 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=2V3−V3=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
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Hence, option
(b) is correct answer.