Problem 64PE

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 in order to obtain a certain intensity projected on the bathroom floor. The ceiling s 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.

Solution 64PE

Calculate the resistance offered by each heat lamp working at a power of 250 W and 120 V voltage is applied across the parallel combination of four lamps if one lamp gets burned. What is the magnification of the object when distance between the object and mirror is 10 cm and the distance between the image and mirror is 3 m . Calculate the area of the image formed if the area of the object is 100 and the intensity of the infrared radiation used.

Since, remaining three bulbs still work if one bulb burns, so these bulbs are connected in parallel. Place filament of bulb at focal point of concave mirror to produce parallel beam on bathroom floor.

The current is,

Here I is current in ampere, W is power in watt, and V is voltage in volts.

Substitute 250 W for W and 120 V for V in equation,

Solve,

= 2.1 A

Resistance is given as,

Here R is resistance, V is voltage, and I is the current.

Substitute 120 V for V and 2.1 A for I in equation,

Solve,

= 57 ohms

The magnification is given as

Here m is magnification, is the image distance, and is the object distance.

Substitute 3.0 m for and 10 cm for .

=30

Calculate the image area from relation,

Substitute 30 for m and 100 for A,

= (30) (100

= 0.300

Calculate the intensity of IR radiation is,

Substitute 250 W for P and 0.300 for ,

= 416. 667 W/

Hence, the intensity of IR radiation is 416.667 W/