Physics - Current Electricity Question with Solution | TestHub

The formula to calculate the resistance of the original wire is given by

$R=\rho \frac{l}{A}...\left(1\right)$

When the new wire is formed, its resistance is given by

$R^{\prime }=\rho \frac{l^{\prime }}{4\text{A}}...\left(2\right)$

Divide equation (2) by equation (1) and simplify to obtain the expression for the new resistance.

$$\begin{array}{rlr}\frac{R^{\prime }}{R}& =\frac{\rho \frac{l^{\prime }}{4A}}{\rho \frac{l}{A}}& \\ & \Rightarrow & R^{\prime }=R\frac{l^{\prime }}{4l}...\left(3\right)\end{array}$$

Substitute the values of the known parameters into equation (3) to calculate the required new resistance.

$$\begin{array}{rl}{R}^{\prime }& =\frac{\frac{l}{4}}{4l}\times 160\Omega \\ & =10\Omega \end{array}$$