Question

two conductors of length 20 cm and 16 cm of mass 200 grams and hundred grams and are made of the same material find the ratio of their resistance
A. 2:1
B.4:1
C.25:32
D.5:4​

Answer 1

May be the answer is b

Answer 2

Answer:

The ratio of their resistance is 25:32.

(c) is correct

Explanation:

Given that,

Length of first conductors = 20 cm

Length of second conductors = 16 cm

Mass of first conductor = 200 gm

Mass of second conductor = 100 gm

Two conductors are made of the same material.

We know that,

The resistance of the conducting wire is equal to the product of the resistivity of the material and length of the wire divided by the area of cross section.

The formula is defined as:

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

Multiply by l on both sides

$R=\dfrac{\rho l^2}{A\times l}$....(I)

We know that,

The volume is defined as:

$V = \dfrac{m}{\rho}$

Put the value of volume in equation (I)

$R=\dfrac{\rho l^2}{\dfrac{m}{\rho}}$

$R=\dfrac{\rho^{2}l^2}{m}$

The resistance for first conductor

$R_{1}=\dfrac{\rho^{2}l_{1}^2}{m_{1}}$

$R_{1}=\dfrac{\rho^{2}\times(20)^2}{200}$.....(II)

The resistance for second conductor

$R_{2}=\dfrac{\rho^{2}\times(16)^2}{100}$....(III)

The ratio of their resistance is

$\dfrac{R_{1}}{R_{2}}=\dfrac{\rho^2\times(20)^2}{200}\times\dfrac{100}{\rho^2\times(16)^2}$

$\dfrac{R_{1}}{R_{2}}=\dfrac{20\times20\times100}{200\times16\times16}$

$\dfrac{R_{1}}{R_{2}}=\dfrac{25}{32}$

Hence, The ratio of their resistance is 25:32.