Question

9. Masses of three wires of copper are in the ratio of 1: 3:5 and their lengths are in the ratio
of 5: 3:1. The ratio of their electrical resistance is
(2) 1 : 15 : 125
(1) 125: 15:1
(4) 1:3:5
(3) 5:3 : 1

​

Answer 1

Answer:

Resistance of wire R=ρ

A

L

where ρ is the resistivity of wire

Using A=

L

V

and V=

d

m

where d is the density of material of wire

We get R=ρd

m

L

2

⟹ R∝

m

L

2

Thus ratio of resistances R

1

:R

2

:R

3

=

m

1

L

1

2

:

m

2

L

2

2

:

m

3

L

3

2

∴ R

1

:R

2

:R

3

=

1

5

2

:

3

3

2

:

5

1

2

⟹ R

1

:R

2

:R

3

=125:15:1