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# Circ rlc paralel

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bazele electrotehnicii

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• ### Circ rlc paralel

1. 1. Unit 25 R-L-C Parallel Circuits
2. 2. Unit 25 R-L-C Parallel Circuits <ul><li>Objectives: </li></ul><ul><li>Discuss parallel circuits that contain resistance (R), inductance (L), and capacitance (C). </li></ul><ul><li>Compute the values of an R-L-C parallel circuit. </li></ul><ul><li>Compute all circuit values. </li></ul>
3. 3. Unit 25 R-L-C Parallel Circuits <ul><li>Objectives: </li></ul><ul><li>Discuss the operation of a parallel resonant circuit. </li></ul><ul><li>Compute the power factor correction for an AC motor. </li></ul>
4. 4. Unit 25 R-L-C Parallel Circuits <ul><li>In the R-L-C parallel circuit, the voltage is the same across all the component branches. However, the currents through the branches will have a phase shift based on the various component properties. </li></ul><ul><li>Inductive current lags the voltage. </li></ul><ul><li>Capacitive current leads the voltage. </li></ul><ul><li>Resistive current is in phase with the voltage. </li></ul>
5. 5. Unit 25 R-L-C Parallel Circuits Phase relationships of current and voltage.
6. 6. Unit 25 R-L-C Parallel Circuits R-L-C parallel circuit schematic.
7. 7. Unit 25 R-L-C Parallel Circuits <ul><li>Circuit Values </li></ul><ul><li>Z = total impedance of the circuit </li></ul><ul><li>I T = total circuit current </li></ul><ul><li>I R = resistor current flow </li></ul><ul><li>P = true power (watts) </li></ul><ul><li>L = inductance of the inductor </li></ul><ul><li>I L = inductor current flow </li></ul><ul><li>VARs L = reactive power of the inductor </li></ul>
8. 8. Unit 25 R-L-C Parallel Circuits <ul><li>Circuit Values </li></ul><ul><li>C = capacitance of the capacitor (farads) </li></ul><ul><li>I C = capacitor current flow </li></ul><ul><li>VARs C = reactive power of the capacitor </li></ul><ul><li>VA = volt-amperes (apparent power) </li></ul><ul><li>PF = power factor </li></ul><ul><li>angle θ = degrees of phase shift (theta) </li></ul>
9. 9. Unit 25 R-L-C Parallel Circuits <ul><li>Impedance </li></ul><ul><li>Z = 1 / √ (1/R) 2 + (1/X L – 1/X C ) 2 </li></ul><ul><li>Z = R x X / √( R 2 + X 2 ) </li></ul><ul><li>Inductance and Inductive Reactance </li></ul><ul><li>L = X L / 2 π F and X L = 2 π FL </li></ul><ul><li>Capacitance and Capacitive Reactance </li></ul><ul><li>C = 1 / 2 π F X C and X C = 1 / 2 π FC </li></ul>
10. 10. Unit 25 R-L-C Parallel Circuits <ul><li>Resistive Current </li></ul><ul><li>I R = E / R </li></ul><ul><li>Inductive Current </li></ul><ul><li>I L = E / X L </li></ul><ul><li>Capacitive Current </li></ul><ul><li>I C = E / X C </li></ul>
11. 11. Unit 25 R-L-C Parallel Circuits Vector diagram of currents.
12. 12. Unit 25 R-L-C Parallel Circuits Reducing vector currents.
13. 13. Unit 25 R-L-C Parallel Circuits <ul><li>True Power </li></ul><ul><li>P = E x I R </li></ul><ul><li>Reactive Power </li></ul><ul><li>VARs Total = √(VARs L – VARs C ) 2 </li></ul><ul><li>Apparent Power </li></ul><ul><li>VA = E x I T </li></ul><ul><li>VA = √P 2 + (VARs L – VARs C ) 2 </li></ul>
14. 14. Unit 25 R-L-C Parallel Circuits <ul><li>Power Factor </li></ul><ul><li>PF = Watts / VA </li></ul><ul><li>Angle Theta </li></ul><ul><li>Cosine θ = PF </li></ul>
15. 15. Unit 25 R-L-C Parallel Circuits Example circuit #1 values.
16. 16. Unit 25 R-L-C Parallel Circuits Example circuit #2 given values.
17. 17. Unit 25 R-L-C Parallel Circuits <ul><li>Parallel Resonance </li></ul><ul><li>Parallel resonant circuits are often called tank circuits. The special properties of this circuit can be used to heat treat sections of metal pipe and welds. </li></ul>
18. 18. Unit 25 R-L-C Parallel Circuits Example resonant circuit at 1200 Hz.
19. 19. Unit 25 R-L-C Parallel Circuits Tank circuit with circulating current.
20. 20. Unit 25 R-L-C Parallel Circuits Induction heating system.
21. 21. Unit 25 R-L-C Parallel Circuits Frequency controls heat penetration depth.
22. 22. Unit 25 R-L-C Parallel Circuits <ul><li>Power Factor Correction </li></ul><ul><li>Power factor correction can be done at either the load or the service. In each situation a capacitor or capacitor bank is connected in parallel. </li></ul>
23. 23. Unit 25 R-L-C Parallel Circuits Determining motor power factor.
24. 24. Unit 25 R-L-C Parallel Circuits Equivalent motor circuit.
25. 25. Unit 25 R-L-C Parallel Circuits Capacitor used to correct motor PF.
26. 26. Unit 25 R-L-C Parallel Circuits <ul><li>Review: </li></ul><ul><li>The voltage applied to all legs of an R-L-C parallel circuit is the same. </li></ul><ul><li>The current flow in the resistive leg will be in phase with the voltage. </li></ul><ul><li>The current flow in the inductive leg will lag the voltage by 90 °. </li></ul><ul><li>The current flow in the capacitive leg will lead the voltage by 90°. </li></ul>
27. 27. Unit 25 R-L-C Parallel Circuits <ul><li>Review: </li></ul><ul><li>Angle theta for the circuit is determined by the amounts of inductance and capacitance. </li></ul><ul><li>An L-C resonant circuit is often referred to as a tank circuit. </li></ul><ul><li>When an L-C parallel circuit reaches resonance, the line current drops and the total impedance increases. </li></ul>
28. 28. Unit 25 R-L-C Parallel Circuits <ul><li>Review: </li></ul><ul><li>When an L-C parallel circuit becomes resonant, the total circuit current is determined by the amount of pure resistance in the circuit. </li></ul><ul><li>Total circuit current and total impedance in a resonant tank circuit are proportional to the Q of the circuit. </li></ul>
29. 29. Unit 25 R-L-C Parallel Circuits <ul><li>Review: </li></ul><ul><li>Motor power factor can be corrected by connecting capacitance in parallel with the motor. The same amount of capacitive VARs must be connected as inductive VARs. </li></ul>
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