Question

A wire of resistance 1 ohm is stretched twice its length. Then the percentage increase in its resistance is
a.100%
b.200%
c.300%
d.400%​

Answer 1

Resistance of a wire is given by

R = (ro)* L/A

where (ro) is the resistivity of the metal,

L is thr length of wire

A is the cross section area of wire.

now, let initially the wire was of length L and cross section area A

R = (ro)*L/A = 1 ohm

the length of the wire is doubled. However, the quantity of metal in wire is same so when length is doubled there must be decrease in cross section area of wire.

new length = 2L

let new cross section area = A1

now, colume of wire will remain same

(wire is cylindrical so volume is cross sectional area x length)

A1*2L = AL

A1 = A/2

new resistance = (ro) (2L)/(A/2)

= (ro)*2*2*L/A

= 4*(ro)*L/A

= 4*1

= 4 ohm

increase in resistance = 4 - 1 = 3 onm

percentage increase = 3/1*100

= 300%

Answer 2

Answer:

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