Six similar bulbs are connected as shown in the figure with a DC source of emf E and zero internal resistance.

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 :

Accepted Answer

(i) All bulbs are glowing: The equivalent resistance $R_{eq} = \frac{R}{3} + \frac{R}{3} = \frac{2R}{3}$. Power $P_i = \frac{E^2}{R_{eq}} = \frac{3E^2}{2R}$. (ii) Two from section A and one from section B are glowing: The equivalent resistance $R_{eq} = \frac{R}{2} + R = \frac{3R}{2}$. Power $P_f = \frac{E^2}{R_{eq}} = \frac{2E^2}{3R}$. The ratio $\frac{P_i}{P_f} = \frac{3E^2}{2R} 	imes \frac{3R}{2E^2} = 9 : 4$.

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