The resistance of a wire is ohm. If it is melted and stretched to times its original length, its new resistance will be [2017]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
The resistance of a wire is $' R'$ ohm. If it is melted and stretched to $' n'$ times its original length, its new resistance will be [2017]

1 $\frac{R}{n}$

2 $n^{2} R$

3 $\frac{R}{n^{2}}$

4 $n R$

Ans.
(2)

The resistance of a wire of length $l$ and area $A$ and resistivity $ρ$ is given as

$R = \frac{ρ l}{A}$

Given, $l' = n l$

As the volume of the wire remains constant

$∴$ $A' l' = A l or A' = \frac{A l}{l'} = \frac{A l}{n l} or A' = \frac{A}{n}$

$∴$ $R' = \frac{ρ l'}{A'} or R' = \frac{ρ n l}{\frac{A}{n}} = \frac{n^{2} ρ l}{A} = n^{2} R$

Want Us to Email you About Special Offers & Updates?