Question

Two conductors of a and b have their length in ratio 4;3 and area of cross section ratio 1:2 and resistivities in ratio 2:3 find the ratio of their resistance

Answer 1

✿ AnSwer:

Ratio of their resistance is 16 : 9

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➤Provided:

It is given that length of two conductors are in ratio 4:3 while ratio of area of cross section of two conductors is 1 : 2 also the ratio of resistivity of the conductors is 2 : 3.

➤To Find:

• Ratio of their resistance.

➤Solution:

Let us assume that the ratio of the length be 4a :3a also,ratio of the area of cross section of two conductors be b : 2b and the ratio of the resistivity of two conductors 2c : 3c.

As we know,

$\bigstar \: { \boxed{ \sf{Resistance = \dfrac{ \rho \: l}{A}}}}$

The Resistance of the first conductor =$\sf \: R = \dfrac{2c \times 4a}{b}$

The Resistance of the second conductor = $\sf \: R' = \dfrac{3c\times 3a}{2b}$

Now,

Ratio of their resistance :

$: \implies \: \sf \dfrac{R }{R' } = \dfrac{ \dfrac{2c \times 4a}{b} }{\dfrac{3c \times 3a}{2b}}$

$: \implies \: \sf \: \dfrac{R}{R'} = \dfrac{2c \times 4a \times 2b}{3c \times 3a \times b}$

$: \implies \: \sf \: \dfrac{R}{R' } = \dfrac{16}{9}$

Hence, ratio is 16 : 9.

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