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?

Answer 1

Original resistance, $R=3\Omega$
Original length, $l=10cm$

New length, $l^{\prime }=30cm=3l$

Let the new cross-sectional area and resistance be $A^{\prime }$ and $R^{\prime }$.

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

So, $lA=l^{\prime }{A}^{\prime }\Rightarrow 30\times A^{\prime }=10\times A\Rightarrow A^{\prime }=\frac{A}{3}$

Original resistance, $R=\frac{\rho l}{A}$

New resistance, $R^{\prime }=\frac{\rho l^{\prime }}{A^{\prime }}=\frac{\rho \times 3l}{\frac{A}{3}}=9\frac{\rho l}{A}=9\times 3=27\Omega$