Question

a wire of given material having length L and radius of cross section r has a resistance of 6 ohm. what would be the resistance of another wire of the same material having length L/2 and radius of cross section 3r ?​

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=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