Question

A wire of resistance 9 ohm having length 30 cm is tripled on itself. What is its new resistance?

Answer 1

Given,

Original resistance, $R=9\Omega$
Original length, $l=30cm$
New length, $l^{\prime }=\frac{30}{3}=10cm$

Therefore, the area of cross-section also becomes 3 times, i.e.;

New area = $A^{\prime }=3A$

We know that,

$R=\rho \frac{l}{A}$

$R_{New}=\rho \frac{l^{\prime }}{A^{\prime }}$

$\Rightarrow R_{New}=\rho \frac{l/3}{3A}=\frac{1}{9}\times \rho \frac{l}{A}=\frac{1}{9}\times R$

$\therefore R_{New}=\frac{1}{9}\times 9=1\Omega$.