Question

A wire of given material having length land area of cross-section A
has a resistance of 4 Q2. What would be the resistance of another wire
of the same material having length 1/2 and area of cross-section 2A?​

Answer 1

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

Answer 2

Answer:

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