Question

Two wires of the same material have their lengths in the ratio
of 2:3 and the radii in the ratio of 8:9. Calculate the ratio of
the currents through them, when equal potential difference is
applied separately between their ends.

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Answer 1

Nice question

We know that Current flowing through conductor is inversely proportional to resistance

V = RI

I = 1 / R

Or can be written as ( I1 / I2 = R2 / R1 )

Also resistance = ρ L / A

On combining,

I1 / I2 = (A1×L2) / (L1×A2)

I1 / I2 = (8×3) / (9×2)

Hence the ratio is 4:3