JEE Main · 2004 · 24 Apr 2004 · Offline · Current Electricity

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An electric current is passed through a circuit containing two wires of the same material, connected in parallel. If the length and radii of the wires are in the ratio of

4/3

and

2/3

, then the ratio of the currents passing through the wire will be

(A)3
(B) $1/3$ ✓ Correct
(C) $8/9$
(D)2

Answer: (B)

Solution

In parallel the two wires share the same voltage, so the currents divide inversely as the resistances,

\frac{I _{1}}{I _{2}} = \frac{R _{2}}{R _{1}}

. With

R = ρ \frac{L}{π r ^{2}}

, the ratio of resistances is

\frac{R _{1}}{R _{2}} = \frac{L _{1}}{L _{2}} \cdot \frac{r _{2}^{2}}{r _{1}^{2}} = \frac{4}{3} \cdot (\frac{3}{2})^{2} = \frac{4}{3} \cdot \frac{9}{4} = 3

. Hence

\frac{I _{1}}{I _{2}} = \frac{R _{2}}{R _{1}} = \frac{1}{3}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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