Question

A cylindrical conductor of length l and area of cross section A has resistance R another conductor of length 2.5 l and resistance 0.5 of the same material has area of cross section??

Answer 1

Given that,

A cylindrical conductor of length l and area of cross section A has resistance R.

To find,

The area of cross section of another conductor of length 2.5 l and resistance 0.5 of the same material.

Solution,

The resistance of a material is given by :

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

If l' = 2.5l and R' = 0.5 R, let A' is the area. New resistance is given by :

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

Solving for A'

$A'=\dfrac{\rho l'}{R'}$ ....(2)

Plugging all the values,

$A'=\dfrac{\rho (2.5)l}{(0.5R)}$ .....(2)

Dividing (1) by (2)

$\dfrac{A'}{A}=\dfrac{\dfrac{\rho (2.5)l}{(0.5R)}}{\dfrac{\rho l}{R}}\\\\\dfrac{A'}{A}=5\\\\A'=5A$

So, the new area will be 5 times of the initial area.

Answer 2

Answer:

Explanation:

HELLO DEAR,

A cylindrical conductor of lengh = l

Cross section area = A

Resistance = R

By using formula of ohms law,

R = Pl/A. ( P = resistivity)

So, resistance of above conductor is given by R = Pl/A

P = RA/ l..........i)

Resistance of anothe conductor is given = 0.5

Lenght of conductor = 2.5l

To find its Cross section Area= A1

So, by using ohms law ,

R = Pl/A1

0.5 = (P×2.5l) / A1

A1= (P×2.5l)/0.5 .........ii)

By putting the value of resistiviy( P ) of the fisrt material in equation ii) to find its area, because both conductor of same material .So resistivity of both material is same.

Now A1 =( P×2.5l)/0.5

A1 = (RA/l × 2.5l)/0.5

A1= (2.5RA)/0.5 answer.

I HOPE IT HELP YOU DEAR,

THANKS.