Question

a bulb is made using two filaments. A switch selects whether the filaments are used individually or in paralell. when used with a 15V battery, the bulb can be operated at 5W, 10W, or 15W. what should be the resistances of the filaments?

Answer 1

Let R₁ and R₂ be the resistances of the filaments in the bulb individually and R₃ be the equivalent resistance of the two resistances which is selected by the switch.
Given :
V = 15 V
Case 1 :
When the switch selects first resistance R₁, then power of the bulb, P₁ = 5 W
Using formula :
P = $\frac{V^2}{R}$
$$\begin{gathered} R_1=\frac{V^2}{P_1} \\ weget{R}_1=\frac{(15{)}^2}{5}=49\Omega \end{gathered}$$
Case 2 :

When the switch selects second resistance R₂, then power of the bulb, P₂ = 10 W
​using above formula, we get R₂ = 22.5 Ω

Case 3 :
When the switch selects the filaments of resistances R₁ and R₂ in parallel connection , then the equivalent resistance of the both resistances is R₃ and power of the bulb P₃ = 15 W
​R₃ = V²/P₃ = 225/15 = 15 ​ Ω