First slide

Thermal effect of current

Question

Two electric bulbs rated P₁ and P₂ watt at V volt are connected in series across V volt mains, then their total power consumption P is:

Moderate

A

$(P_{1} + P_{2})$
B

$\sqrt{P_{1} P_{2}}$
C

$\frac{P_{1} P_{2}}{(P_{1} + P_{2})}$
D

$\frac{(P_{1} + P_{2})}{P_{1} P_{2}}$

Solution

Resistance of Ist bulb $= R_{1} = \frac{V^{2}}{P_{1}}$
Resistance of IInd bulb $= R_{2} = \frac{V^{2}}{P_{2}}$
When both bulbs are connected in series,
$R_{eq .} = V^{2} [\frac{1}{P_{1}} + \frac{1}{P_{2}}] = \frac{V^{2} (P_{1} + P_{2})}{P_{1} P_{2}}$
Hence, power consumed $P = \frac{V^{2}}{R}$
$= \frac{V^{2}}{V^{2} (\frac{P_{1} + P_{2}}{P_{1} P_{2}})} = \frac{P_{1} P_{2}}{P_{1} + P_{2}}$
Hence, (c) is correct.

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