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Transcript
AC Circuits Summary Average values (root mean square) Vrms avg (V 2 ) Vmax 2 avg for sin2 or cos2 = 1/2 Transformers: V2 N 2 V1 N1 Energy conservation Power: I1 V2 N 2 I 2 V1 N1 P1 P2 I1V1 I 2V2 Ohm’s Law: V = I Z Z = impedence, combined resistance and reactance. Reactance, ω dependent: Capacitors X C 1 C Inductors: X L L Phase difference means combination requires PythagoreanTheorem: 2 1 Z R L in Ohms C 2 Phase difference also means that the amplitude of the power is less than the (voltage amplitude) · (current amplitude); Prms I rmsVrms cos( phase difference) Filters: Low Pass High Pass VC high at low ω (RC > 1/ω to charge) VL high at high ω (V ~ ΔI/Δt ~ ω) Oscillator 1 LC Approach 1: Remember the spring and mass oscillator. When the mass is at the maximum or minimum spring extension, the stored potential energy in the spring is a maximum and the mass is momentarily at rest. When the mass passes through the equilibrium position, the velocity is at maximum and the potential energy is zero. At max or min position, the spring exerts a force to move the mass. At equilibrium position, the force is zero, but the momentum carries the mass past that point to continue the oscillations. For the LC circuit, the capacitor stores potential energy as charge builds up on the plates. The inductor resists changes in the current, so it keeps current flowing when the charge (and therefore the voltage) on the capacitor is zero. Energy Force Continue motion Spring & mass Potential, Kinetic Spring momentum LC circuit E field, B Field Voltage on Capacitor Inductor Approach 2: Follow the change in electrical values. Vc + max +, decreasing 0 -, increasing -max Current direction changing Current direction changing -,decreasing 0 This is plotted below: I 0 ΔI/Δt +max VL -max + increasing +max + decreasing 0 + decreasing 0 - decreasing -max - decreasing 0 + decreasing +max -increasing -max - decreasing 0 +decreasing 0 Notice that the voltage across the inductor is a quarter cycle ahead of the current and the current is a quarter cycle ahead of the voltage on the capacitor. When we used to use E for voltage, the mnemonic for remembering this was “ELI the ICE man” {E leads I for L; I leads E for C} Animation of current flow: http://www.falstad.com/circuit/index.html Shows fields oscillating http://www.walter-fendt.de/ph11e/osccirc.htm Circuit info. and animation http://www.allaboutcircuits.com/vol_2/chpt_6/5.html