Question

If a copper wire is stretched to make it 0.1% longer. The percentage change in its resistance is

• A. 0.2% increase
• B. 0.2% decrease
• C. 0.1% increase
• D. 0.1% decrease

Answer 1

Step 1: Given data and formula used
Resistance, $R=\frac{\rho l}{A}$
where $\rho$ is resistivity, $l$ is original length and $A$ is cross sectional area of wire.
Multiplying and dividing by length $l$
$R=\frac{\rho l^2}{A\times l}=\frac{\rho l^2}{V}$
Step 2: Calculation of Percentage change in resistance,
%$R=\frac{R^{\prime }-R}{R}$
$R^{\prime }=\frac{\rho \left(1.001l^2\right)}{V}$ $\because ($New length, $l^{\prime }=l+\frac{0.1}{100}l=1.001l)$
$R=\frac{\rho l^2}{V}$
$\Rightarrow$ %$R=\frac{{\frac{\rho \left(1.001l^2\right)}{V}}^{\prime }-\frac{\rho l^2}{V}}{\frac{\rho l^2}{V}}\times 100$
%$R=0.2001$%
Hence resistance increase by 0.2%.

The correct option is B 0.2% increase