Question

A wire of given material having length L and area of cross-section A has a resistance of 8Ω. What would be the resistance of another wire of the same material having length 2L and area of cross-section A/2?​

Answer 1

Answer:

Wire of uniform cross-section has a resistance of R. Let the diameter be d,  the length of the wire be l cross-sectional area be A.

Now the resistance of a wire can be expressed as:

R=ρAl

Where resistivity is ρ.

Now a second wire is twice as long and of half cross section.

Let final length be l1, diameter be d1 and

cross section Area be A1.

A1=2A

R1=ρA1l1

Putting the value of l1=2l and A1=2A

We have, resistance of the new second wire, R2=ρA4l=4×R1=4×8=32Ω

Explanation:

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