Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10-8 Ω m and wire Y is made of a metal of resistivity 5.6 × 10-8 Ω m.

Question 12

Two wires have the same length and the same resistance. Wire X is made of a metal of resistivity 1.7 × 10^-8 Ω m and wire Y is made of a metal of resistivity 5.6 × 10^-8 Ω m.

The diameter of wire X is 0.315 mm.

What is the diameter of wire Y?

A 0.17 mm                  B 0.33 mm                  C 0.57 mm                  D 1.0 mm

Reference: Past Exam Paper – June 2017 Paper12 Q34

Solution:

Answer: C.

Resistance R = ρL / A

Cross-sectional area A = πd² / 4

The two wires have the same resistance and same length.

Resistance of wire X = Resistance of wire Y

1.7×10^-8 × L / (π×(0.315²)/4) = 5.6×10^-8 × L / (π×(d²)/4)

Cancelling the common terms,

1.7×10^-8 / 0.315² = 5.6×10^-8 / d²

d² = (5.6×10^-8 / 1.7×10^-8) × 0.315²  

Diameter of wire Y: d= √[(5.6×10^-8 / 1.7×10^-8) × 0.315²]

 
Diameter d = 0.57 mm