Question

71. The masses of the 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 [CBSE AIPMT 1988) (a) 1:3:5 (b) 5:3:1 (c) 1:25: 125 (d) 125:15:1​

Answer 1

Answer:

125

:

15

:

1

Mass, M =Volume

×

Density

⇒

M

=

A

l

×

d

, where A is area of cross-section and l is the length.

or

A

=

M ya

l

d

Resistance of a wire,

R

=

ρ

l

A

=

ρ

l

(

M

l

d

)

=

ρ

l

2

d

M

As all the three wire are made up of same material (i.e. copper) therefore

ρ

and d are same for all the three wires.

∴

R

∝

l

2

M

∴

R

1

:

R

2

:

R

3

=

l

2

1

M

1

:

l

2

2

M

2

:

l

2

3

M

3

=

5

2

1

:

3

2

3

:

1

2

5

=

25

:

3

:

1

5

=

125

:

15

:

1

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