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?
A 0.17 mm B 0.33 mm C 0.57 mm D 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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