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?

Answer 1

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:
$$\begin{gathered} R_1=\frac{{\left(15\right)}^2}{5}=45\mathrm{\Omega } \\ {R}_2=\frac{{\left(15\right)}^2}{10}=22.5\mathrm{\Omega } \\ {R}_3=\frac{{\left(15\right)}^2}{15}=15\mathrm{\Omega } \end{gathered}$$
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.