Question

The electric resistance of a certain wire of iron is R if it's length and radius are both doubled then what will be the new resistance

Answer 1

Answer:

The electric resistance of a certain wire of iron is R, if it's length and radius are both doubled then the new resistance will be the half of the previous resistance .

Explanation:

We know that,

R1 = ρl1/A1

Where R1 = current resistance of the wire.

           l1 =current length of the wire.

           A1 =(πr²) current cross-sectional area of the wire.

When the length and the radius are both doubled then,

A2 = π(2r)² = 4πr² = 4A1

l2 = 2l1

Let the new resistence be R2.

So,

R1/R2 = (ρl1/A1) / (ρl2/A2)

          = (ρl1/A1) / (2ρl1/4A1)

          = 2

R2 = R1/2.