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The resistance of a given wire is $24 Ω$ . What will be its new resistance if (a) only the length of a conductor is increased to $3$ times of its original length, and (b) only the cross-section area of the wire is doubled?

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72 Ω, 12 Ω

70 Ω, 16 Ω

75 Ω, 14 Ω

77 Ω, 10 Ω

answer is A.

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Detailed Solution

New resistance will be

72 Ω, 12 Ω

.
Given data in the problem,
Resistance,

R = 24 ohm

Condition (a) when the length of wire increased by

3

times of its original length
Assuming that the original length of wire is l and it is increased by

3

times. As we know that resistance depends upon the length of the conductor, the resistance for this wire is

3 R

.
So,
Resistance,

R = 3 \times 24

\Rightarrow R = 72 ohm

Condition (b) when cross-section area is doubled
Assuming the area of the wire is A, and it is double of its original area. So, the new area is

2 A

. We know that resistance decreases as area increases.
So,
Resistance

= \frac{24}{2}

Resistance

= 12

ohm
So,
Resistance when length of wire increased by

3

times of its original length

= 72

ohm
Resistance when cross-section area is doubled

= 12

ohm.

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