A filament bulb $(500 \,W,\,\, 100 \,V)$ is to be used in a $230\, V$ main supply. When a resistance $R$ is connected in series, it works perfectly and the bulb consumes $500\,W.$ The value of $R$ is .................. $\Omega$
NEET 2016, Medium
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Resistance of bulb, $R_{B}=\frac{V^{2}}{P}=\frac{(100)^{2}}{500}=20\, \Omega$
Power of the bulb in the circuit,
$P =V I $
$I =\frac{P}{V_{B}} $
$=\frac{500}{100}=5\, \mathrm{A}$
$V_{R} =I R \Rightarrow(230-100)=5 \times R $
$\therefore \quad R =26 \,\Omega$
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