Question

If on stretching wire its radius decreases by 1%, the resistance will

• A. increase by $1$%
• B. increase by $2$%
• C. increase by $4$%
• D. not change

Answer 1

Answer: (C)

increase by $4$%

Wider wires have a greater cross-sectional area. The wider the wire, the less resistance that there will be to the flow of electric charge. When all other variables are the same, charge will flow at higher rates through wider wires with greater cross-sectional areas than through thinner wires.
In this case, the wire is stretched and the radius of the wire is decreased by $1$%.
The relation between the resistance and the area of cross section of the wire is given as follows.
$R=\frac{\rho L}{A}==\frac{\rho L\times A}{A\times A}=\frac{\rho V}{A^2}$

$R\propto \frac{1}{A^2}$, where A is the area of cross section of the wire.
Area is calculated by squaring the radius. Therefore, the above relation can be written as $R\propto \frac{1}{r^4}$.
Hence, for a small change in radius $r$, the % change in the resistance $R$ is equal to (-4) times % change in r.

Here, the % change in radius is $-1$. So, the % change in resistance is$(-4)(-1)=+4$%

The resistance will be increased by 4%.