phy mc electric

2009-11-08 10:04 pm
Two copper wires, A and B, of the same length have the ratio of mass of 4 : 9. Assuming the cross-sectional are uniform, what is the ratio of the resistance of A to that of B ? (1989-34)

A. 2 : 3
B. 3 : 2
C. 4 : 9
D. 9 : 4
E. 16 : 81

回答 (1)

2009-11-08 11:01 pm
✔ 最佳答案
Since resistance R = r.L/A
where r is the resistivity of copper
L is the length of wire
A is the cross-sectional area

and mass m = d.(AL), d is the density of copper
i.e. A = m/d.L

hence, R = r.L(d.L/m) = r.d.L^2/m
that is, given r, d and L are constants, resistance R is inversely proportional to m

R(A)/R(B) = mass(B)/mass(A) = 9/4


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