A filament bulb (500 W, 100 V) is to be used in a 230 V main supply. When a resistance is connected in series, it works perfectly and the bulb consumes 500 W. The value of is [2016]

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Solution

Q.
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 [2016]

1 230 Ω

2 46 Ω

3 26 Ω

4 13 Ω

Ans.
(3)

Resistance of bulb, $R_{B} = \frac{V^{2}}{P} = \frac{{(100)}^{2}}{500} = 20$ $Ω$

Power of the bulb in the circuit,

$P = V I; I = \frac{P}{V_{B}}; I = \frac{500}{100} = 5 A$

$V_{R} = I R \Rightarrow (230 - 100) = 5 \times R ∴ R = 26 Ω$

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