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# Two electric bulbs, one of 200V, 40W, and the other 220V, 100W are connected in a house wiring circuitA) They have equal currents through themB) The resistance of the filaments of both the bulb is the sameC) The resistance of the filament of 40 W bulb is more than that of 100 Watt bulbD) The resistance of the 100 W bulb is more than the 40-watt bulb

Last updated date: 20th Jun 2024
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Hint: Electric bulbs are connected in parallel with each other to an external power supply. We will use the relation of power dissipated across a resistor to find the resistance of the bulb. For two bulbs in parallel, they have the same

Now when two bulbs are connected in parallel, they have the same potential difference across the branches containing them. However, the current flowing through them is not necessarily equal and depends on the resistance of the bulbs. If both the bulbs have the same resistance, then the current flowing through them will be the same. So, let us calculate the resistance of the two bulbs.
We know that the relation of power, voltage, and resistance is given as
$P = \dfrac{{{V^2}}}{R}$
We can rewrite the above equation as
$R = \dfrac{{{V^2}}}{P}$
For bulb 1, the resistance will be
${R_1} = \dfrac{{{{200}^2}}}{{40}}$
$\Rightarrow {R_1} = 1000\,\Omega$
And for bulb 2, the resistance will be
${R_2} = \dfrac{{{{220}^2}}}{{100}}$
$\Rightarrow {R_2} = 484\,\Omega$
So, the resistance isn’t equal but rather bulb 1 has a higher resistance than bulb 2. Alternatively, we can say that the resistance of the filament in the 40 W bulb (bulb 1) is higher than the resistance of the filament in the 100 W bulb (bulb 2).
So the correct choice is option (C).

Note
We should realize that bulbs in a household are connected in parallel with the external power supply to solve this question. This is done because if one of the bulbs fails, the circuit can still function and other bulbs will still get current flowing through them. The resistances of the bulb are often defined in this manner in practical scenarios instead of in ohms.