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Series resistance needed to run a rated bulb or lamp on a higher supply voltage

This type of question, asked 3 times: 2021 Paper 14, 2021 Paper 19, 27 Jun 2022. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 14

    13
    A bulb rated 200W, 100 V100\text{ }V is connected to 200 V200\text{ }V supply. What external resistance should be connected in series to have same power as earlier?

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  2. Question 2

    2021 Paper 19

    15
    An electric bulb of 500 watt at 100 volt is used in a circuit having a 200 V200\text{ }V supply. Calculate the resistance RR to be connected in series with the bulb so that the power delivered by the bulb is 500 W500\text{ }W.

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  3. Question 3

    27 Jun 2022

    22
    A 220 V,50 Hz220\text{ }V,50\text{ }Hz AC source is connected to a 25 V25\text{ }V, 5 W5\text{ }W lamp and an additional resistance RR in series (as shown in figure) to run the lamp at its peak brightness, then the value of RR (in ohm) will be