    Question

# A $50W$ bulb is in series with a room heater and the combination is connected across the mains. To get max. heater output, the $50W$ bulb should be replaced by

A

$20W$

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B

$10W$

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C

$100W$

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D

$200W$

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Solution

## The correct option is D $200W$ Step 1: Given dataPower of the bulb $P=50W$Let $i$ be the current.Let $V$ be the voltage.Let ${R}_{1}$ be the resistance of the bulb.Let ${R}_{2}$ be the resistance of the heater.Step 2: Relation between heat and resistanceWe know that heating in a circuit is given as$H={i}^{2}R={\left(\frac{V}{{R}_{1}+{R}_{2}}\right)}^{2}{R}_{2}$We can see that, $H\propto \frac{1}{{R}_{1}}$.Therefore to get a maximum heating output, the $50W$ bulb should be replaced by the highest-rated power bulb i.e. $200W$.Hence, the correct answer is option (D).  Suggest Corrections  1      Similar questions  Explore more