Question

Nichrome wire of length L and radius R has resistance of 10 Ohm. How would the resistance of the wire change when: a) Only length of the wire is doubled? b) Only diameter of the wire is doubled? Justify your answer.​

Answer 1

Answer:

Explanation:

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

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