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RLC Circuits

RLC Circuits. PH 203 Professor Lee Carkner Lecture 24. RCL and AC. w d = 2 p f X C = 1/( w d C) X L = w d L If you combine a resistor, capacitor and an inductor into one series circuit, they all will have the same current but all will have difference voltages at any one time

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RLC Circuits

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  1. RLC Circuits PH 203 Professor Lee Carkner Lecture 24

  2. RCL and AC wd = 2pf XC = 1/(wdC) XL = wdL • If you combine a resistor, capacitor and an inductor into one series circuit, they all will have the same current but all will have difference voltages at any one time • Voltages are all out of phase with each other

  3. RLC Circuit

  4. RLC Impedance • Called the impedance (Z) Z = (R2 + (XL - XC)2)½ • The voltages for the inductor and capacitor are 180 degrees opposed and so subtract V = IZ • Can think of Z as a generalized resistance for any AC circuit

  5. Time Dependence • The instantaneous value (v, i) • The maximum value (V, I) • The root-mean-squared value (Vrms, Irms) • However, the average of a sinusoidal variation is 0

  6. Since power depends on I2 (P =I2R) it does not care if the current is positive or negative Irms = I/(2)½ = 0.707 I Vrms = V/(2)½ = 0.707 V The rms value is about 71% of the maximum Finding rms

  7. Phase Angle and Power Factor • They are separated by a phase anglef, often written as: cos f = IR/IZ = R/Z • But I and V are out of phase and sometime they reinforce each other and sometimes they cancel out • Can write power as: Pav = IrmsVrms cos f • We just need to know V and I through it at a given time

  8. High and Low f • For high f the inductor acts like a very large resistor and the capacitor acts like a resistance-less wire • At low f, the inductor acts like a resistance-less wire and the capacitor acts like a very large resistor • No current through C, full current through L

  9. Natural Frequency • Example: a swing • If you push the swing at all different random times it won’t • If you connect it to an AC generator with the same frequency it will have a large current

  10. Resonance • This condition is known as resonance • Low Z, large I (I = V/Z) Z = (R2 + (XL - XC)2)½ • This will happen when wd = 1/(LC)½ • Frequencies near the natural one will produce large current

  11. Resistance and Resonance • Note that the current still depends on the resistance • at resonance, the capacitor and inductor cancel out • If we change R we do not change the natural frequency, but we do change the magnitude of the maximum current • Since the effect of L and C are smaller in any case

  12. Next Time • Read 32.1-32.5 • Problems: Ch 31, P: 45, 46, 61, Ch 32, P: 12, 14

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