A $100 W / 200 V$ bulb and an inductor are connected in series to a $220 V / 50 H z$ supply. Find the power consumed by the bulb.

100 W

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92 W

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84 W

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74 W

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Solution

The correct option is C $74 W$
$P = I^{2} R = {(\frac{V}{| Z |})}^{2} R$
$= {(\frac{220}{\sqrt{(400)^{2} + (100 π)^{2}}})}^{2} \times 400;$
$R = \frac{200^{2}}{100} = 400 Ω$
$\Rightarrow \frac{484 \times 10^{2} \times 400}{16 \times 10^{4} \times 10 \times 10^{4}} = \frac{1936}{26} = 74.46 W$

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A 100W/200V bulb and an inductor are connected in series to a 220V/50Hz supply. Find the power consumed by the bulb.

The correct option is C 74WP=I2R=(V|Z|)2R=(220√(400)2+(100π)2)2×400; R=2002100=400Ω⇒484×102×40016×104×10×104=193626=74.46W

A $100 W / 200 V$ bulb and an inductor are connected in series to a $220 V / 50 H z$ supply. Find the power consumed by the bulb.

The correct option is C $74 W$
$P = I^{2} R = {(\frac{V}{| Z |})}^{2} R$
$= {(\frac{220}{\sqrt{(400)^{2} + (100 π)^{2}}})}^{2} \times 400;$
$R = \frac{200^{2}}{100} = 400 Ω$
$\Rightarrow \frac{484 \times 10^{2} \times 400}{16 \times 10^{4} \times 10 \times 10^{4}} = \frac{1936}{26} = 74.46 W$