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Lecture 31b - Chapter 31 Simple AC circuits Resistor...

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Chapter 31: Simple AC circuits
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R R V I R Resistor circuits Notation: Use lowercase for instantaneous values, Uppercase for peak values v R = ε = V R sin ω t i R = v R /R = I R sin ω t In an AC circuit, resistor voltage and current oscillate in phase . ε = ε m sin ω t
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Capacitor circuits v C = ε = V C sin ω t i = dq/dt and q = Cv C : i C = ω CV C cos ω t which we write as: i C = ω CV C sin ( ω t + π /2) The current leads voltage by π /2 rads ICE ε = ε m sin ω t Current reaches peak value I C the instant the capacitor is fully discharged and v C =0. The current is zero the instant the capacitor is fully charged.
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Capacitive Reactance Relationship between peak current and voltage in a capacitor I C = ω CV C , although they don’t happen at the same time. Define the capacitive reactance X C = 1/ ω C, then: I C = V C /X C This is analogous to Ohm’s Law for DC. at very high frequencies, X C approaches 0 and the capacitor acts like a wire. Units of X C :
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Consider this circuit. The frequency of the AC source is adjusted, while its voltage amplitude is kept constant. The light bulb will glow brightest at A. High frequencies B. Low frequencies C. The brightness will be the same at all frequencies 1 C X C
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