A wire has a resistance of 10 ohm . If it is stretched by one-tenth of its original length, then its

Question

A wire has a resistance of 10 ohm . If it is stretched by one-tenth of its original length, then its resistance will be\

Professor PC Thomas Classes · Answer

Let original length be 100 L and original area $=\mathrm{A}$. Then $10=\frac{ho(100 \mathrm{~L})}{\mathrm{A}}$ When the length increases $10 \%$ it becomes 110 L , Let $\mathrm{A}^{\prime}$ be the new area. Then\ $R=\frac{ho(110 L)}{A}$\ $\frac{\mathrm{R}}{10}=\frac{110}{100} 	imes \frac{\mathrm{A}}{\mathrm{A}^{\prime}}$\ Volume is always constant\ $	herefore 100 	imes \mathrm{A}=110 	imes \mathrm{A}^{\prime}$\ $	herefore \frac{\mathrm{A}}{\mathrm{A}^{\prime}}=\frac{110}{100}$\ $	herefore \frac{\mathrm{R}}{10}=\frac{110}{100} 	imes \frac{110}{100}=1.21$\