Question

The resistance of a 20 cm long wire is 5 $\Omega$. The wire is stretched to form a uniform wire of 40 cm length. The resistance now will be :

• A. $5\Omega$
• B. $10\Omega$
• C. $20\Omega$
• D. $200\Omega$

Answer 1

Answer: (C)

$20\Omega$

The resistance of a wire is given by $R=\rho \frac{l}{A}$

where $\rho$ is the resistivity of the material

$l$ is the length of the wire

$A$ is the cross sectional area of the wire

Since stretching of a wire does not change the volume of the wire,

$V=lA=constant$

$⟹A=\frac{V}{l}$

Thus $R=\rho \frac{l}{V/l}=\rho \frac{l^2}{V}\propto l^2$

Since the length of wire doubles, the resistance becomes four times = $20\Omega$