Question

A wire of given material having length l and area of cross section.A resistance of
$4\pi$
what would be the resistance of another wire of the same material having length 1/2 and area of cross section 2A ?


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Answer 1

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Answer 2

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=ρ

A

l

Where resistivity is ρ.

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

Let final length be l

1

, diameter be d

1

and

cross section Area be A

1

.

A

1

=

2

A

R

1

=ρ

A

1

l

1

Putting the value of l

1

=2l and A

1

=

2

A

We have, resistance of the new second wire, R

2

=ρ

A

4l

=4×R

1

=4×8=32Ω