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Two electric bulbs rated at (25 W, 220 V) and (100 W, 220 V) are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P₁& P₂ respectively, then

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a

$P_{1} = 9 W, P_{2} = 16 W$

b

$P_{1} = 16 W, P_{2} = 4 W$

c

$P_{1} = 4 W, P_{2} = 16 W$

d

$P_{1} = 16 W, P_{2} = 9 W$

answer is B.

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Detailed Solution

$\begin{array}{l} R_{25} = \frac{V^{2}}{P_{1}} = \frac{220 \times 220}{25} = 1936 Ω \\ R_{100} = \frac{V^{2}}{P_{2}} = \frac{220 \times 220}{100} = 484 Ω \\ R_{eq} = R_{25} + R_{100} = 2420 Ω \\ I = \frac{V}{R} = \frac{220}{2420} = 0 .09 A \\ P_{25} = I^{2} R_{25} = 0 .09 \times 0 .09 \times 1936 = 16 W \\ P_{100} = I^{2} R_{25} = 0 .09 \times 0 .09 \times 484 = 4 W \end{array}$

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