First slide

Electrical power

Question

Two electric bulbs each of rating 60 W, 200 V are connected in series and a 100 volt d.c. supply is connected across the combination. Then total power consumed by the combination is

Moderate

A

45 W
B

30 W
C

7.5 W
D

15 W

Solution

Resistance of each bulb $R = \frac{V^{2}}{P}$
$∴$ Equivalent resistance, $R_{C} = R + R = \frac{2 V^{2}}{P}$
$∴$ Power $= P^{1} = \frac{{(V^{1})}^{2}}{R_{C}} = \frac{{(V^{1})}^{2}}{2 V^{2} / P} = \frac{P}{2} {(\frac{V^{1}}{V})}^{2} = \frac{60}{2} {(\frac{100}{200})}^{2} W = 7.5 W$

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