Question

Two wires a and b of same material and same mass have radius 2r and r if the resistance of wire a

Answer 1

Hii there,

# Complete question -

Q. Two wires a and b of same material and same mass have radius 2r and r if the resistance of wire a is 34 ohm. Find the resistance of wire b.

◆ Answer -

Rb = 544 ohm

● Explanation -

As both wires are made of same material & same mass, both will have same volume.

Let l be the length of wire A.

V = la × Aa

V = l × π(2r)^2

V = l × 4πr^2

Let l' be the length of wire B.

V = lb × Ab

V = lb × πr^2

V = lb × πr^2

l' = V / πr^2

lb = l × 4πr^2 / πr^2

lb = 4l

Ratio of resistance of wire A to wire B is -

Ra/Rb = (ρ.la/Aa) / (ρ.lb/Ab)

Ra/Rb = la.Ab / lb.Aa

Ra/Rb = (l × πr^2) / (4l × 4πr^2)

Ra/Rb = 1/16

Rb = 16 Ra

Therefore, resistance of wire B will be -

Rb = 16 × 34

Rb = 544 ohm.

Thanks...