Question

A wire of length is 1m it's resistance is 4ohms .find the resistance if specific resistance Is doubled and diameter I'd doubled the length is 3times the first

Answer 1

Answer:

The resistance becomes 1.5 times, therefore the answer is 6 ohms.

Explanation:

The formula for resistance in terms of specific resistance is,

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

                  where, $\rho$  = specific resistance

                              l = length

                               a = area of cross section

Given,                      

            $\rho _2=2\rho_1$    (∵ specific resistance is doubled)

           $l_2=3l_1$   (∵ length becomes three times)

            $\begin{array}{l}d_2=2d_1\\\begin{aligned}\therefore a_2=4a_1\\\ \end{aligned}\end{array}$   (∵ diameter doubled , so area becomes four times)

⇒        $R_2=\rho _2\frac{l_2}{a_2}$    → (1)

Substitute for $\rho _2\ ,\ l_{2\ },\ a_2$ in equation (1)

    ⇒        $R_2=2\rho _1\times \frac{3l_1}{4a_1}$

               $\therefore R_2=\frac{3}{2}R_1=\frac{3}{2}\times 4=6\Omega$