First slide

Vertical circular motion

Question

Six similar bulbs are connected as shown in the figure with a DC source of emf E, and zero internal resistance. The ratio of power consumption by the bulbs when (i) all are glowing and (ii) in the situation when two from section A and one from section B are glowing, will be

Moderate

A

2 : 1
B

4 : 9
C

9 : 4
D

1 : 2

Solution

$Power consumed, P = i^{2} R {(P_{eq})}_{1} = (i / 3)^{2} \times 3 R + (i / 3)^{2} \times 3 R = \frac{2}{3} i^{2} R . . . . . . (i) (ii) {(P_{eq})}_{2} = (i / 2)^{2} \times R + (i / 2)^{2} R + i^{2} R = \frac{3}{2} i^{2} R . . . . . . . . . (ii)$
$Divide equation (i) by (ii), we get \frac{{(P_{eq})}_{1}}{{(P_{eq})}_{2}} = \frac{\frac{2}{3} i^{2} R}{\frac{3}{2} i^{2} R} = \frac{4}{9}$

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