First slide

Electrical power

Question

Two identical electric bulbs, each of rating series and a 200 volt d.c. source is connected across the combination. Then power consumed by each bulb is

Moderate

A

100 W
B

50 W
C

25 W
D

12.5 W

Solution

Resistance of each bulb, $R = \frac{V^{2}}{P}$
Current through each bulb, $i = \frac{V_{1}}{2 R} = \frac{{PV}_{1}}{2 V^{2}}$
Power consumed by each bulb $P' = i^{2} R = {(\frac{{PV}_{1}}{2 V^{2}})}^{2} \times \frac{V^{2}}{P} = \frac{P}{4} {(\frac{V_{1}}{V})}^{2} = \frac{50}{4} {(\frac{200}{100})}^{2} walt \Rightarrow P' = 50 wa t t$

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