* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download A Brief History of Planetary Science
Power inverter wikipedia , lookup
Ground (electricity) wikipedia , lookup
Electrical substation wikipedia , lookup
Spark-gap transmitter wikipedia , lookup
Stepper motor wikipedia , lookup
Opto-isolator wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Flexible electronics wikipedia , lookup
Chirp spectrum wikipedia , lookup
Integrated circuit wikipedia , lookup
Circuit breaker wikipedia , lookup
Current source wikipedia , lookup
Utility frequency wikipedia , lookup
Resonant inductive coupling wikipedia , lookup
Earthing system wikipedia , lookup
Mains electricity wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Three-phase electric power wikipedia , lookup
Zobel network wikipedia , lookup
Electrical ballast wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Regenerative circuit wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Alternating current wikipedia , lookup
RLC Circuits Physics 102 Professor Lee Carkner Lecture 25 Three AC Circuits DVmax = 10 V, f = 1Hz, R = 10 DVrms = 0.707 DVmax = (0.707)(10) = R = Irms = DVrms/R = Imax = Irms/0.707 = Phase Shift = When V = 0, I = DVmax = 10 V, f = 1Hz, C = 10 F DVrms = 0.707 DVmax = (0.707)(10) = XC = 1/(2pfC) = 1/[(2)(p)(1)(10)] = Irms = DVrms/XC = Imax = Irms/0.707 = Phase Shift = When V = 0, I = I max = Three AC Circuits DVmax = 10 V, f = 1Hz, L = 10 H DVrms = 0.707 DVmax = (0.707)(10) = XL = 2pfL = (2)(p)(1)(10) = Irms = DVrms/XL = Imax = Irms/0.707 = Phase Shift = When V = 0, I = I max = For capacitor, V lags I For inductor, V leads I RLC Circuits Z = (R2 + (XL - XC)2)½ The voltage through any one circuit element depends only on its value of R, XC or XL however RLC Circuit RLC Phase The phase angle f can be related to the vector sum of the voltages Called the power factor RLC Phase Shift Also: tan f = (XL - XC)/R The arctan of a positive number is positive so: Inductance dominates The arctan of a negative number is negative so: Capacitance dominates The arctan of zero is zero so: Resistor dominates Frequency Dependence The properties of an RLC circuit depend not just on the circuit elements and voltage but also on the frequency of the generator Frequency affects inductors and capacitors exactly backwards High f means capacitors never build up much charge and so have little effect High and Low f For “normal” 60 Hz household current both XL and XC can be significant 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 resistanceless wire and the capacitor acts like a very large resistor High and Low Frequency Today’s PAL a) How would you change Vrms, R, C and w to increase the rms current through a RC circuit? b) How would you change Vrms, R , L and w to increase the rms current through a RL circuit? c) How would you change Vrms, R , and w to increase the current through an RLC circuit? d) What specific relationship between L and C would produce the maximum current through a RLC circuit? LC Circuit The capacitor discharges as a current through the inductor This plate then discharges backwards through the inductor Like a mass on a swing LC Resonance Oscillation Frequency Since they are connected in parallel they must each have the same voltage IXC = IXL w = 1/(LC)½ This is the natural frequency of the LC circuit 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 Resonance Will happen when Z is a minimum Z = (R2 + (XL - XC)2)½ This will happen when w = 1/(LC)½ Frequencies near the natural one will produce large current Impedance and Resonance Resonance Frequency Resistance and Resonance Note that the current still depends on the resistance So at resonance, the capacitor and inductor cancel out Peak becomes shorter and also broader Next Time Read 22.1-22.4, 22.7 Homework, Ch 21, P 71, Ch 22, P 3, 7, 8