Question

1 point
2. A metallic conductor with
resistance 'R' is divided into 3
equal parts. Afterwards these
parts are connected in parallel
Its total resistance is R'. Then R:
R' is *
O A)1:3
O B) 9:1
O C) 1:9
OD) 3:1​

Answer 1

Answer:

1:3is the ratio

hope it helps you

Answer 2

R : R' = 9 : 1

Therefore, option (B) is correct.

Explanation:

Given:

A metallic conductor R is divided into 3 equal parts and then these parts are connected in parallel. The total resistance is R'

To find out:

The ratio  R : R'

Solution:

For a wire of a material, the resistivity is constant while its resistance can change. the resistance depends upon the length (l), cross sectional area (A) and resistivity (ρ), then

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

If the wire is divided into 3 equal parts, the length of each part will be l/3

while its cross sectional area will remain the same

Hence, the resistance of each part will be

$r=\rho\frac{l/3}{A}$

$\implies r=\frac{1}{3}\times\rho\frac{l}{A}$

$\implies r=\frac{1}{3}R$

Now these wires are connected in parallel and the combined resistance is R'

Thus,

$\frac{1}{R'}=\frac{1}{R/3}+\frac{1}{R/3}+\frac{1}{R/3}$

$\implies \frac{1}{R'}=\frac{3}{R}+\frac{3}{R}+\frac{3}{R}$

$\implies \frac{1}{R'}=\frac{3+3+3}{R}$

$\implies \frac{1}{R'}=\frac{9}{R}$

$\implies\frac{R}{R'}=\frac{9}{1}$

$\implies R:R'=9:1$

Hope this answer is helpful.

Know More:

Similar Questions:

https://brainly.in/question/40361373

https://brainly.in/question/40370812