Question

Nichrome wire of length L and radius r has resistance of 10 ohms . How would the resistance of wire change when 1)only length of the wire is doubled 2)only diameter of the wire is doubled ?justify your answer

Answer 1

Given :
length =L
resistance= 10 ohms
radius =r

1] )only length of the wire is doubled  :

We know that : 

R=ρ L/A

Let the new resistance be : R1

R1 =ρ(2 L)/A =2 ρ L/A=2R=2x10=20 ohms

So if only  the length of Ni chrome  wire doubles the , Resistance becomes doubles.
R=20 ohms

2]only diameter of the wire is doubled:

R=ρ L/A
When diameter doubles, radius of wire also doubles.A=πr²A1=π(2r)² =4 π r²=4A

The new resistance will be :R2=ρL/4A=R/4=10/4=2.5ohms

Answer 2

hope it helps.................