Question

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

• A. $27\Omega$.
• B. $9\Omega$.
• C. $3\Omega$.
• D. $30\Omega$.

Answer 1

The correct option is A $27\Omega$.

On stretching a wire, both its area of cross-section and length changes but its volume remains constant.

$R_1=3\Omega$ , $l_1=10cm$ , $l_2=30cm=3l_1$

And, $A=\frac{V}{l}$

Now, $R=\rho \frac{l}{A}$

$⟹R=\rho \frac{l^2}{V}$

$⟹R\propto l^2$

On increasing length to 3 times of initial value.

Hence, $\frac{R_2}{R_1}=\frac{l_2^2}{l_1^2}=9$

$⟹R_2=9R_1=9\times 3\Omega$

$R_2=27\Omega$

Answer-(A)