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
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