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,

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,

TestHub · Accepted Answer

Case (i): When all bulbs are glowing, then,

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

Then, initially power consumption will be from the equation,

Power $P = \frac{E^{2}}{R}$

$P_{i} = \frac{E^{2}}{R_{e q}} = \frac{3 E^{2}}{2 R} . . . (1)$

Case (ii): When two bulbs in section $A$ and one bulb in the section are glowing,

$R_{eq}^{'} = \frac{R}{2} + R = \frac{3}{2} R$
$P_{f} = \frac{E^{2}}{R_{eq}^{'}} = \frac{2 E^{2}}{3 R} . . . (2)$

From above two equations, ratio of power is,

$\frac{P_{i}}{P_{f}} = \frac{9}{4}$

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