Question

A tungsten wire has resistance R at 20°C. A second tungsten wire at 20°C has twice the length and half the cross-sectional area of the first wire. In terms of R, the resistance of the second wire is

Answer 1

Answer:

Resistance will become 4 times of first wire resistance.

Explanation:

At the temperature of both the the tungsten wire is same so we can apply ohm's law

Let the length of first wire is $l_1$ and cross sectional area is $A_1$

Resistance of first wire $R=\frac{\rho l_1}{A_1}$......1

Now length of second wire is twice the length of first wire

$l_2=2l_1$ and cross sectional area $A_2=\frac{A_1}{2}$.......2

Resistance of wire 2 $R_2=\frac{\rho l_2}{A_2}$........2

Dividing equation 1 by equation 1

$\frac{R}{R_2}=\frac{\rho l_1}{A_1}\times \frac{0.5A_1}{\rho 2l_1}$

$R_2=4R$

Therefore resistance will become 4 times.