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Physics-

General

Easy

Question

What is the potential difference across 2 $mu$ F capacitor in the circuit shown?

12 V
4 V
6 V
18 V

The correct answer is: 6 V

Net emf in the circuit here
$E equals E subscript 2 end subscript minus E subscript 1 end subscript equals 16 minus 6 equals 10$ volt
While the equivalent capacity
$C equals blank fraction numerator C subscript 1 end subscript C subscript 2 end subscript over denominator C subscript 1 end subscript plus C subscript 2 end subscript end fraction equals blank fraction numerator 2 cross times 3 over denominator 2 plus 3 end fraction equals fraction numerator 6 over denominator 5 end fraction mu F$
Charge on each capacitor
$q equals C V equals fraction numerator 6 over denominator 5 end fraction cross times 10 equals 12 mu C$
$therefore$ Potential difference across $2 mu F$ capacitor
$V subscript 1 end subscript equals fraction numerator q over denominator C subscript 1 end subscript end fraction equals fraction numerator 12 over denominator 2 end fraction equals 6 blank v o l t$

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