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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 13.5V
Length =3cm (L1)=60mm
5cm(L2)=100mm
radii =1mm(r1)=0.5mm
=3m(r2)=1.5mm
The EMF of the battery =16V
material is same so resistivity would also be same
Air1L1=A
A1R1L1=A2R2L2
A1=π(0.5)×0.5=0.25Pi
R1R2=A2L1A1L2
R1R2=2.25π×600.25π×100
or, R1R2=225×6025×100
or R1R2=5.4=5410=275
(Hence, R1=27 and R2=5)
Since they are in series R1+R2=27+5=32
i=VR
i=1632=12=0.5A
Now, Pd across 6cm wire is
V=iR
=0.5×27
=13.5V

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