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

Q#12 (Past Exam Paper – June 2017 Paper12 Q34)

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?
0.17 mm                  0.33 mm                  0.57 mm                  1.0 mm



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

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