Resistance of a wire is R and cross section area is A now areas change to N times. What will be the new resistance?

Given that

Resistance of a wire is R and cross-section area is A now areas change to N times.

We need to find new resistance.

We know that

Resistance,R = ρl/A

Where,

ρ=Resistivity of the wire
l=lenght of wire
A= cross-section of the wire
When we increase the length of wire by n times

Let us assume the initial and final radius of the wire be r1,&r2 respectively.

Irrespective of increase in length the volume remains the same

Since the initial and final volume are equal

2π(r1^2)l = 2π(r2^2)(nl)

So, r2=r1/√n

So, the cross-sectional area becomes 1/n times the initial value.

Substituting the values in the formula for resistance, we get

new resistance n2 times greater than the initial value of resistance.

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