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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 data

Power of the bulb P=50W

Let i be the current.

Let V be the voltage.

Let R1 be the resistance of the bulb.

Let R2 be the resistance of the heater.

Step 2: Relation between heat and resistance

We know that heating in a circuit is given as

H=i2R=VR1+R22R2

We can see that,

H1R1.

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).


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