$A$ piece of wire is redrawn,without change in volume,so that its radius is halved. Compare the new resistance with the original resistance.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(D) Let the length of the original wire be $l$ and its radius be $r$.
The original resistance is given by $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$.
The original volume is $V_1 = \pi r^2 l$.
When the radius is halved,the new radius becomes $r' = \frac{r}{2}$. Let the new length be $l'$.
Since the volume remains constant,$V_1 = V_2$,so $\pi r^2 l = \pi (\frac{r}{2})^2 l'$.
$\pi r^2 l = \pi \frac{r^2}{4} l'$,which simplifies to $l' = 4l$.
The new resistance is $R' = \rho \frac{l'}{\pi (r')^2} = \rho \frac{4l}{\pi (r/2)^2}$.
$R' = \rho \frac{4l}{\pi (r^2/4)} = 16 \left( \rho \frac{l}{\pi r^2} \right)$.
Therefore,$R' = 16R$.
The new resistance is $16$ times the original resistance.

Explore More

Similar Questions

Two bulbs are marked $60\, W, 220\, V$ and $100\, W, 220\, V$. These are connected in parallel to a $220\, V$ mains. Which one out of the two will glow brighter?

In an electrical circuit,three incandescent bulbs $A, B$ and $C$ of rating $40 \, W, 60 \, W$ and $100 \, W$ respectively are connected in parallel to an electric source. Which of the following is likely to happen regarding their brightness?

An electric bulb is connected to a $220 \ V$ generator. The current is $0.50 \ A$. What is the power of the bulb?

$(a)$ State $Ohm's$ law. Express it mathematically.
$(b)$ Write symbols used in electric circuits to represent:
$(i)$ Variable resistance.
$(ii)$ Voltmeter.
$(c)$ An electric bulb is rated $220 \, V$ and $100 \, W$. When it is operated on $110 \, V$,what will be the power consumed?

Why is tungsten metal selected for making filaments of incandescent lamps?

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo