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Lesson 20 Series AC Circuits

Lesson 20 Series AC Circuits. Learning Objectives. Compute the total impedance for a series AC circuit. Apply Ohm’s Law, Kirchhoff’s Voltage Law and the voltage divider rule to AC series circuits. Graph impedances, voltages and current as a function of phase.

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Lesson 20 Series AC Circuits

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  1. Lesson 20Series AC Circuits

  2. Learning Objectives • Compute the total impedance for a series AC circuit. • Apply Ohm’s Law, Kirchhoff’s Voltage Law and the voltage divider rule to AC series circuits. • Graph impedances, voltages and current as a function of phase. • Graph voltages and current as a function of time.

  3. Review Impedance • Impedance is a complex quantity that can be made up of resistance (real part) and reactance (imaginary part). Z = R + jX = Z () • Unit of impedance is ohms ().

  4. Review Resistance • For resistors, voltage and current are in phase.

  5. Review • For inductors, voltage leads current by 90º.

  6. Review • For capacitors, voltage lags current by 90º.

  7. Impedance • Because impedance is a complex quantity, it can be represented graphically in the complex plane. ZR = R0º = R + j0 = R ZL = XL90º = 0 + jXL = jXL ZC = XC-90º = 0 - jXC = -jXC

  8. ELI the ICE man Current Current Voltage Voltage Inductance Capacitance I leads E E leads I Since the voltage on a capacitor is directly proportional to the charge on it, the current must lead the voltage in time and phase to conduct charge to the capacitor plate and raise the voltage When voltage is applied to an inductor, it resists the change of current. The current builds up more slowly, lagging in time and phase.

  9. Solving complex EE problems • Convert sine waves to phasors • Perform multiplication/division if needed • Convert phasors to complex numbers if needed to perform addition/subtraction • Convert back to phasor form for the answer to the problem

  10. Important Notes • Peak values are useful for time domain representations of signals. • RMS values are the standard when dealing with phasor domain representations • If you need to represent something in the time domain, you will need to convert RMS->Peak voltage to obtain Em

  11. Example Problem 1 For the circuit below: • Time Domain voltage and current v(t) and i(t) • Draw the sine waveforms for v and i • Draw the phasor diagram showing the relationship between V and I

  12. Example Problem 1 i(t)=50 sin (20000t) mA v(t)=25 sin (20000t -90°) V 314 μsec

  13. AC Series Circuits • Total impedance is sum of individual impedances. • Also note that current is the same through each element.

  14. Impedance example

  15. Impedance example

  16. Special case of Impedance • Whenever a capacitor and inductor of equal reactances are placed in series, the equivalent circuit is a short circuit.

  17. Impedance • If the total impedance has only real component, the circuit is said to be resistive (X = 0 or  = 0°). • But since • If  > 0°, the circuit is inductive. ELI • If  < 0°, the circuit is capacitive. ICE

  18. Example Problem 2 A network has a total impedance of ZT=24.0kΩ-30˚ at a frequency of 2 kHz. If the network consists of two series elements, what types of components are those and what are their R/L/C values?

  19. Kirchhoff’s Voltage Law (KVL) • The phasor sum of voltage drops and rise around a closed loop is equal to zero. KVL

  20. Voltage Divider Rule (VDR)

  21. Example Problem 3 es(t)=170 sin (1000t + 0) V. Determine ZTOT Determine total currentITOT Determine voltages VR, VL, and Vc Verify KVL for this circuit Graph E, VL, VC, VR in the time domain

  22. Example Problem 3 180° phase difference between L and C

  23. Example Problem 4 es(t)=294 sin (377t + 0) V. • Use the voltage divider rule to find VL • Determine the value of inductance

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