Question

The lengths of two wires made of same material are 2 m and 1 m.Their radii are 1 mm and 2 mm. The ratio of their specific resistances is:

• A. 2 : 1
• B. 1 : 2
• C. 4 : 1
• D. 1 : 1

Answer 1

Answer: (A)

2 : 1

Given that,

Length of the wire $l_1=2m$

Length of the wire $l_2=1m$

Radii of the wire $r_1=1mm$

Radii of the wire $r_2=2mm$

We know that,

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

Now, the specific resistances for both wires

$R_1=\frac{{\rho }_1{l}_1}{A_1}$

$R_2=\frac{{\rho }_2{l}_2}{A_2}$

As material is same of both wires

So, $R\propto \frac{l}{A}$

Where, $A=\pi r^2$

Now, the ratio of specific resistance is

$\frac{R_1}{R_2}=\frac{\rho l_1\times A_2}{\rho l_2\times A_1}$

$\frac{R_1}{R_2}=\frac{1\times r_2^2}{2\times r_1^2}$

$\frac{R_1}{R_2}=\frac{1\times 4}{2\times 1}$

$\frac{R_1}{R_2}=\frac{2}{1}$

Hence, the ratio of specific resistance is $2:1$