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Q.

An electric current of 5A is divided in three branches forming a parallel combination. The lengths of the wires in the three brancehes are in the ratio 2 : 3 : 4 and their diameters are in the ratio 3 : 4 : 5. Find the currents in each branch if the wires are of the same material.

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a

1.40 A; 1.66 A; 1.94 A

b

1.50 A; 1.76 A; 2.04 A

c

1.70 A; 1.96 A; 2.24 A

d

1.60 A; 1.86 A; 2.14 A

answer is A.

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Detailed Solution

1.40 A; 1.66 A; 1.94 A
$\begin{array}{l} R_{1} : R_{2} : R_{3} = \frac{l_{1}}{d_{1}^{2}} : \frac{l_{2}}{d_{2}^{2}} : \frac{l_{3}}{d_{3}^{2}} \\ = \frac{2}{9} : \frac{3}{16} : \frac{4}{25} \\ i_{1} : i_{2} : i_{3} = 108 : 128 : 150 \\ i_{1} = \frac{5 \times 108}{382} = 1 .41 A \\ i_{2} = \frac{5 \times 128}{382} = 1 .67 A \\ i_{3} = \frac{5 \times 150}{20} = 1 .96 A \end{array}$

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