Question

When the resistance wire is passed through a die the cross-section area decreases by 1%, the change in resistance of the wire is

• A. 1% decrease
• B. 1 % increase
• C. 2 % decrease
• D. 2 % increase

Answer 1

The correct option is D 2 % increase

We know,

$R=\frac{\rho L}{A}$

Where L is the length & A is the cross section area of the wire

So, $V=L\cdot A$

$\therefore L=\frac{V}{A}$

$R=\frac{\rho }{A}\times \frac{V}{A}=\frac{\rho V}{A^2}$

$R_{initial}=\frac{\rho V}{A^2}$

$R_{final}=\frac{\rho V}{(0.99A{)}^2}$

$\therefore Change=R_{final}-R_{initial}=\frac{\rho V}{A^2}[\frac{1}{(0.99{)}^2}-1]$

% of change $=\frac{R_{final}-R_{initial}}{R_{initial}}\times 100=\left[\frac{1}{(0.99{)}^2-1}\right]\times 100$

$\approx 2$%