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Unformatted text preview: Chapter 33 Alternating Current (AC) R, L, C in AC circuits AC, the description c A DC power source, like the one from a battery, provides a potential difference (a voltage) that does not change its polarity with respect to a reference point (often the ground) c An AC power source is sinusoidal voltage source which is described as Here ( ) max v V sin t Δ Δ ω = max v V Δ Δ ω is the instantaneous voltage with respect to a reference (often not the ground). is the maximum voltage or amplitude. is the angular frequency, related to frequency f and period T as 2 2 f T π ω π = = V Δ t V Δ Symbol in a circuit diagram: or v Δ v Δ The US AC system is 110V/60Hz. Many European and Asian countries use 220V/50Hz. Resistors in an AC Circuit, Ohm’s Law The voltage over the resistor: ( ) R max v v V sin t Δ Δ Δ ω = = Apply Ohm’s Law, the current through the resistor: ( ) ( ) max R R max V v i sin t I sin t R R Δ Δ ω ω = = ≡ The current is also a sinusoidal function of time t . The current through and the voltage over the resistor are in phase : both reach their maximum and minimum values at the same time. PLAY ACTIVE FIGURE The power consumed by the resistor is ( ) 2 2 2 2 max R R R R R V v p v i i R sin t R R Δ Δ Δ ω = ⋅ = = = We will come back to the power discussion later. Phasor Diagram, a useful tool. c The projection of a circular motion with a constant angular velocity on the y axis is a sinusoidal function. c To simplify the analysis of AC circuits, a graphical constructor called a phasor diagram is used. A phasor is a vector whose length is proportional to the maximum value of the variable it represents c The phasor diagram of a resistor in AC is shown here. The vectors representing current and voltage overlap each other, because they are in phase. x y O R t ω The projection on the yaxis is ( ) y R R sin t ω = The power for a resistive AC circuit and the rms current and voltage ( ) 2 R max p p sin t ω = ( ) R max v V sin t Δ Δ ω = ( ) R max i I sin t ω = When the AC voltage source is applied on the resistor, the voltage over and current through the resistor are: Both average to zero....
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 Spring '08
 Ye
 Current, Magnetism, Power, Alternating Current, Electrical resistance, Electrical impedance, phasor diagrams, Vmax sin

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