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Question

A wire of resistance 3 ohm and length 10 cm is stretched to length 30 cm. Assuming that it has a uniform cross section, what will be its new resistance?


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Solution

Original resistance, R=3 Ω
Original length, l=10 cm

New length, l=30 cm=3l

Let the new cross-sectional area and resistance be A and R.

On stretching the wire to 30 cm, its volume will remain the same.

So, lA=lA30×A=10×AA=A3

Original resistance, R=ρlA

New resistance, R=ρlA=ρ×3lA3=9ρlA=9×3=27 Ω


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