* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Powerpoint Slides
Standing wave ratio wikipedia , lookup
Regenerative circuit wikipedia , lookup
Spark-gap transmitter wikipedia , lookup
Integrating ADC wikipedia , lookup
Index of electronics articles wikipedia , lookup
Radio transmitter design wikipedia , lookup
Josephson voltage standard wikipedia , lookup
Schmitt trigger wikipedia , lookup
Valve RF amplifier wikipedia , lookup
Wilson current mirror wikipedia , lookup
Operational amplifier wikipedia , lookup
Electrical ballast wikipedia , lookup
Voltage regulator wikipedia , lookup
Power MOSFET wikipedia , lookup
Power electronics wikipedia , lookup
Current source wikipedia , lookup
Opto-isolator wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Resistive opto-isolator wikipedia , lookup
Surge protector wikipedia , lookup
RLC circuit wikipedia , lookup
Lab 8: AC RLC Resonant Circuits DC – Direct Current current Only 4 more labs to go!! time When using AC circuits, inductors and capacitors have a delayed response to the changing voltage and current current AC – Alternating Current time R V = VMAX sin(2ft) I The voltage and current reaches their maximum value at the time. We call this in-phase I time V V Vmax I sin( 2ft ) R R If we average the voltage or current through the resistor over all time the average will be zero! However there will be power dissipated in the resistor. What is important is the root-mean-square, rms-current, rms-voltage I rms I peak 2 Vrms V peak 2 Now we can use all of the regular DC circuit equations we just need to substitute in Irms, and Vrms for I and V. 2 2 rms rms rms rms PI R V I V R Let’s look what happens when we put a capacitor in an AC circuit: C V = VMAX sin(2ft) I So the peak current will occur when V t Q V Q CV I C t t C [Vmax sin( 2ft ) CVmax (2f ) cos( 2ft ) t is a maximum (NOT when the V is maximum). The voltage will lag behind ¼ cycle or 90 degrees. This resistance to current flow is called the capacitive reactance: 1 Xc 2fC Ohm’s law for AC-circuit: This is basically the resistance and is measured in Vrms = Irms XC We can use the same type arguments to anaylze an AC inductor circuit. V L I t In an inductor AC circuit the voltage will be a maximum when the change in current is a maximum. The voltage will lead the current by ¼ cycle or 90 degrees. L V = VMAX sin(2ft) I The inductive reactance is: XL = 2fL Ohm’s Law for an AC-inductor circuit is: Vrms = Irms XL When we attach capacitors, resistors, and inductors in series in an AC circuit the current through each will be the same and will be in phase. This means that the individual voltage drops across each individual element will not be in phase with the current or the total applied voltage. To account for these phase differences we must VL treat the voltages as if they are vectors. Voltage across the inductor, VL +y direction Voltage across the capacitor, VC -y direction Voltage across the resistor, VR + x direction Vtotal V (VL VC ) 2 R 2 VC Vtotal = Vector Sum VL - VC VC VR phase angle: the angle between the total voltage and x-axis tan VL VC VR Just like the voltages add like vectors so to does the resistances of each component: C R R xC xC R L xL Z R 2 X C2 Z Z xL Z R 2 X L2 R XL R L C XC Z Z R2 X L X C 2 XL - XC XC R XL and XC are dependent on frequency, at what frequency does XL = XC ? X L X C 2f R L fR 1 2 4 2 f R LC 1 2f R C 1 2 LC This special frequency is called the resonant frequency. When a circuit operates at it resonant frequency it’s impedance is minimum! Z R 2 X L X C R 2 0 min 2 If Z is a minimum what happens to the current? VLC I will be a maximum! Today you will measure the resonant frequency of a AC RLC circuit. voltage V I Z VR fR frequency