Question

The resistance of a 40 cm long wire is 8 ohm. The wins is stretched to a uniform wire of 60 cm length. The resistance will now be : (a) 18 ohm (b) 16 ohm (d) 2 ohm (C) 8 ohm ​

Answer 1

Correct option is C)

The resistance of a wire is given by R=ρ

A

l

where ρ is the resistivity of the material

l is the length of the wire

A is the cross sectional area of the wire

Since stretching of a wire does not change the volume of the wire,

V=lA=constant

⟹A=

l

V

Thus R=ρ

V/l

l

=ρ

V

l

2

∝l

2

Since the length of wire doubles, the resistance becomes four times = 20 Ω

Answer 2

Answer:

(A). 18 ohm

R final = R original x n²

where n is the number of times wire is stretched

n = 60/4 = 1.5

R final = 8 × 1.5²

= 8 × 2.25

= 18 ohm

so, the answer is 18 ohm