Question

a wire of given material having length L and area of cross section has resistance of 4 what would be the resistance of another wire of same material having 1/2 length and area of cross section 2a

Answer 1

By the formula of resistance:
R=(σ) L/A
here σ is resistivity, L is length of wire and A is area of cross section

Given. σ1=σ2. ______eq 1

for first material R1=σ1 L/A.
we can write.. σ1=R1A/L
σ1=4A/L.

for second material σ2 = R2.4A/L

from eq1. 4A/L=R24A/L
R2=0.

hope you understand
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Answer 2

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We know that the

resistance is P(rho) l/a.

We can ignore P over here because the material is same in both cases.

Now,


R=l/a
4=l/a.


In the second case,

they are asking resistance if the area is double and length is halved.

So, R=l/2

whole divided by 2a.


We get R=l/4a.


But

we l/a=4.

So,


4/4=1

and


so the answer is 1 ohm.