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Question
A bulb is made using two filaments. A switch selects whether the filaments are used individually or in parallel. When used with a 15 V battery, the bulb can be operated at 5 W, 10 W or 15 W. What should be the resistances of the filaments?
Solution
We know:-
\[R = \frac{V^2}{P}\]
where R is the resistance, V is the voltage drop and P is the power on which the bulb is operated.
We can calculate the resistance of the bulb for the same V and different P.
The resistances of the bulb for three different powers are:-
\[R_1 = \frac{\left( 15 \right)^2}{5} = 45 \Omega\]
\[ R_2 = \frac{\left( 15 \right)^2}{10} = 22 . 5 \Omega\]
\[ R_3 = \frac{\left( 15 \right)^2}{15} = 15 \Omega\]
When the two resistance are used in parallel, the equivalent resistance will be less than their individual resistance.
∴ The two resistance are 45 Ω and 22.5 Ω.
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