Question

A uniform wire of length l and radius r

has a resistance of 100 Ω. It is recast into a

wire of radius r/2 . The resistance of new

wire will be :

(1) 1600 Ω

(2) 400 Ω

(3) 200 Ω

(4) 100 Ω

Answer 1

The resistance of new wire will be R’ = 400 ohm.  

Given:

Given data suggests that the length of uniform wire is given as l with radius r and resistance 100 ohm.  

Solution:

It is recasted into wire with radius $\frac{r}{2}$.  

Resistivity of wire material $\begin{array}{r}{\rho, | R=\rho \times \frac{\text {tength}}{\text {area}}} \\ {R=\rho \times \frac{l}{A}} \\ {R=\rho \times \frac{l}{\pi r^{2}}}\end{array}$

New Resistance $\begin{array}{c}{R^{\prime}=\rho \times \frac{l}{\pi r^{2}}} \\ {R^{\prime}=\rho \times \frac{l}{\pi\left(\frac{r}{2}\right)^{2}}} \\ {R^{\prime}=4\left(\rho \times \frac{l}{\pi r^{2}}\right)} \\ {R=100 \text { ohm }} \\ {R^{\prime}=4 \times 100} \\ {R^{\prime}=400 \text { ohm.}}\end{array}$