Simple Nature - Light and Matter

their maxima at the same time. In a lightbulb, the moment ofmaximum power is when the circuit is most rapidly heating thefilament. At the instant when P = 0, a quarter of a cycle later, nocurrent is flowing, and no electrical energy is being turned into heat.Throughout the whole cycle, the filament is getting rid of energy byradiating light. 7 Since the circuit oscillates at a frequency 8 of 60 Hz,the temperature doesn’t really have time to cycle up or down verymuch over the 1/60 s period of the oscillation, and we don’t noticeany significant variation in the brightness of the light, even with ashort-exposure photograph.Thus, what we really want to know is the average power, “average”meaning the average over one full cycle. Since we’re coveringa whole cycle with our average, it doesn’t matter what phase weassume. Let’s use a cosine. The total amount of energy transferredover one cycle is∫E =dEad / Power in a resistor: therate at which electrical energy isbeing converted into heat.=∫ T0dEdt dt ,where T = 2π/ω is the period.E ===∫ T0∫ T0∫ T0P dtP dtI o V o cos 2 ωt dt∫ T= I o V o cos 2 ωt dt0= I o V o∫ T01(1 + cos 2ωt) dt27 To many people, the word “radiation” implies nuclear contamination. Actually,the word simply means something that “radiates” outward. Naturalsunlight is “radiation.” So is the light from a lightbulb, or the infrared lightbeing emitted by your skin right now.8 Note that this time “frequency” means f, not ω! Physicists and engineersgenerally use ω because it simplifies the equations, but electricians and techniciansalways use f. The 60 Hz frequency is for the U.S.Section 10.5 LRC Circuits 611