A bulb is constructed using two filaments. A switch allows the filaments to be used either individually or in parallel. When connected to a 15 V battery, the bulb can operate at 5 W , 10 W , or 15 W . Determine the resistances of the filaments.

Step-by-step solution

The power dissipated by a resistance R across a constant voltage V is given by P = V^2 R . When two filaments are connected in parallel, the total power is the sum of their individual powers, P_p = P₁ + P₂ . Given the possible power outputs are 5 W , 10 W , and 15 W . Since 5 + 10 = 15 , the individual powers of the filaments must be P₁ = 5 W and P₂ = 10 W . The 15 W output corresponds to the filaments connected in parallel. For the first filament, the resistance is: R₁ = V^2 P₁ = 15^2 5 = 225 5 = 45 For the second