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The wattage of a bulb is $24 W$ when it is connected to a $12 V$ battery. What will be its effective wattage, if it operates on a $6 V$ battery? (Neglect the change in resistance due to unequal heating of the filament in the two cases.)

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6 W

5 W

7 W

9 W

answer is A.

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Detailed Solution

The wattage of a bulb is

24 W

when it is connected to a

12 V

battery. Its effective wattage if it operates on a

6 V

battery is

6 W .

The power of a bulb is

P = 24 W

Where the potential difference of battery is

V = 12 V

Resistance of filament of a bulb,

R = \frac{V^{2}}{P}

\Rightarrow R = \frac{12 \times 12}{24}

\Rightarrow R = 6 Ω

When the bulb is operated on a battery of voltage

V^{'} = 6 V

, the effective power of the bulb is given as:

P' = \frac{V^{2}}{R}

\Rightarrow P' = \frac{36}{6}

\Rightarrow P' = 6 W

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