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 a

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Solution

Q.
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 [2019]

1 2 : 1

2 4 : 9

3 9 : 4

4 1 : 2

Ans.
(3)

Let R be the resistance of each bulb.

Case (i)

Net resistance of the circuit, $R_{1} = \frac{R}{3} + \frac{R}{3} = \frac{2 R}{3}$

Power consumption by the bulbs = Power supply by the sources

$\Rightarrow P_{1} = \frac{E^{2}}{(2 R / 3)} = \frac{3 E^{2}}{2 R}$

Case (ii)

Net resistance of the circuit,

$R_{2} = \frac{R}{2} + R = \frac{3 R}{2}$

Power consumption by the bulbs,

$P_{2} = \frac{E^{2}}{(3 R / 2)} = \frac{2}{3} (\frac{E^{2}}{R});$ $\frac{P_{1}}{P_{2}} = \frac{3}{2} \times \frac{3}{2} = \frac{9}{4}$

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