Question

6. Two wires of A and B with circular cross
section made up of the same material
with equal lengths. Suppose R. - 3
then what is the ratio of radius of wire
A to that of B?
(a) 3
(b) √3
(c)1/√3
(d)1/3

Answer 1

Answer:

It is given that two wires of A and B with circular cross section made up of same material with equal length such that,

R_1=3R_2R

1

=3R

2

R is the resistance

\rho \dfrac{l}{A_1}=3\times \rho \dfrac{l}{A_2}ρ

A

1

l

=3×ρ

A

2

l

As material and length are same, there resistivity will be same

\dfrac{1}{\pi r_1^2}=3\times \dfrac{1}{\pi r_2^2}

πr

1

2

1

=3×

πr

2

2

1

\dfrac{1}{r_1^2}=3\times \dfrac{1}{r_2^2}

r

1

2

1

=3×

r

2

2

1

\dfrac{r_1}{r_2}=\dfrac{1}{\sqrt{3} }

r

2

r

1

=

3

1

So, the ratio of the ratio of radius of wire A to that of B is \dfrac{1}{\sqrt{3}}

3

1

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Explanation:

answer is option