1. VSVS L C R At every instant, the generator / supply voltage: (V S = V m sinωt) is given by: V S = V L + V C + V R IZ = IX L + IX C + IR These relationships can best be shown on a PHASOR DIAGRAM

2. RCL I RLC circuit VLVL VRVR VCVC I ω Phasor Diagram

3. See 6 RLC circuits applet

4. LCR Circuit ~ Phasor Diagram VLVL VRVR VCVC I ω V R and I are IN PHASE V L Leads I by 90 o V C LAGS I by 90 o Total reactance (X T ) in the circuit is the difference between X L and X C (X L – X C or X C – X L ) X L - X C XLXL R XCXC R Z

5. VLVL VRVR VCVC VsVs Ф I X T = X L - X C ie X L > X C X T = X C - X L ie X C > X L Phase angle between Voltage supply and Current (or V R )

6. 1.Calculate the reactance of the capacitor 2.Calculate the reactance of the inductor 3.Determine the impedance of the circuit 1.Calculate the reactance of the capacitor 2.Calculate the reactance of the inductor 3.Determine the impedance of the circuit RCL Circuits This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz 15 mH 250 µF 5.0 Ω50 Hz

7. 1.Calculate the reactance of the capacitor RCL Circuits This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz 2.Calculate the reactance of the inductor 15 mH 250 µF 5.0 Ω50 Hz correct sig.fig correct unit

8. X L = 4.7 Ω X C = 13 Ω 8.3 Ω 5.0 Ω 9.7 Ω R = 5.0 Ω OR

9. 1.Determine the supply voltage Vs(rms) 2.Determine the phase difference between the current and the supply voltage 1.Determine the supply voltage Vs(rms) 2.Determine the phase difference between the current and the supply voltage RCL Circuits This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz that provides a current I RMS = 1.2 A This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz that provides a current I RMS = 1.2 A The reactance of the capacitor is 13 Ω, the inductor 4.7 Ω and the impedance of the circuit is 9.7 Ω 15 mH 250 µF 5.0 Ω50 Hz

10. 1.Determine the supply voltage Vs(rms) RCL Circuits This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz that provides a current I RMS = 1.2 A This LCR circuit has a 5.0 Ω resistor in series with a 250 µF capacitor and a 15 mH inductor. The AC supply has a frequency of 50 Hz that provides a current I RMS = 1.2 A The reactance of the capacitor is 13 Ω, the inductor 4.7 Ω and the impedance of the circuit is 9.7 Ω 2.Determine the phase difference between the current and the supply voltage 15 mH 250 µF 50 Hz V R = 5  V C = 13  V L = 4.7  V X = 8.3 x 1.2 V R = 5.0 x 1.2 12 V  By measurement V S lagging current by 60º ± 2º By measurement V S lagging current by 60º ± 2º

11. RCL Example V S = 110 V f = 60 Hz 50  8  F 0.8 H a)What is the impedance of the circuit? b) What is the current in the circuit? c) What is the phase angle between V s and I ?