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Question

# Two wires of the same material have lengths 3 cm and 5 cm and radii 1 mm and 3 mm respectively. They are connected in series across a battery of 16 V. The p.d. across the shorter wire is

A
2.5V
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B
6.5V
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C
1.5V
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D
13.5V
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Solution

## The correct option is D 13.5VLength =3cm (L1)=60mm 5cm(L2)=100mmradii =1mm(r1)=0.5mm =3m(r2)=1.5mmThe EMF of the battery =16Vmaterial is same so resistivity would also be same Air1L1=A A1R1L1=A2R2L2A1=π(0.5)×0.5=0.25PiR1R2=A2L1A1L2R1R2=2.25π×600.25π×100or, R1R2=225×6025×100or R1R2=5.4=5410=275(Hence, R1=27 and R2=5)Since they are in series R1+R2=27+5=32i=VRi=1632=12=0.5ANow, Pd across 6cm wire is V=iR =0.5×27 =13.5V

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