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Two wires made of the same substance are joined in parallel in a circuit. If the ratio of their lengths is 4/3 and the ratio of their radii is 2/3, what is the ratio of the currents flowing through the two wires?

1. 8/9
2. 1/3
3. 3
4. 2

Correct answer: 1/3

Solution

With equal voltage, I = V/R and R = rho L/(pi r^2), so I is proportional to r^2/L. I1/I2 = (r1/r2)^2 x (L2/L1) = (2/3)^2 x (3/4) = (4/9)(3/4) = 1/3.

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