Question

Consider a 250-W heat lamp fixed to the ceiling in a bathroom. If the filament in one light burns out, then the remaining three still work. Construct a problem in which you determine the resistance of each filament to obtain a certain intensity projected on the bathroom floor. The ceiling is 3.0 m high. The problem will need to involve concave mirrors behind the filaments. Your instructor may wish to guide you on the level of complexity to consider in the electrical components.

Answer 1

To determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor, calculate the intensity of the lamp using the power and area of the projection, then determine the resistance of each filament using Ohm's Law.

Step-by-step explanation:

To determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor, we need to consider the power and height of the ceiling.

Let's assume the desired intensity on the floor is I.

First, we can calculate the intensity of the heat lamp using the formula: I = P/A, where P is the power of the lamp and A is the area of the projection on the floor.

Since the lamp has a power of 250 W, we can calculate the area A using the height of the ceiling and the distance from the lamp to the floor.

Once we have the intensity of the lamp, we can determine the resistance of each filament using Ohm's Law:

V = IR, where V is the voltage across the filament (which can be calculated using the power and intensity of the lamp) and R is the resistance of the filament.