Subject : Elements of Electrical Engineering

1. Subject : Elements of Electrical Engineering Department : Electrical Engineering

2. Group’s members Roll No. Name 41. RATIYA RAJU 42. SATANI DARSHANA 43. SAVALIYA MILAN 44. SISARA GOVIND 45. VALGAMA HARDIK 46. VADHER DARSHAK 47. VADOLIYA MILAN 48. VALA GOPAL 49. SHINGADIYA SHYAM 50. KARUD LUKMAN

3. Single phase AC circuit

4. AC Definitions : One effective ampere is that ac current for which the power is the same as for one ampere of dc current. Effective current: ieff = 0.707 imax One effective volt is that ac voltage that gives an effective ampere through a resistance of one ohm. Effective voltage: Veff = 0.707 Vmax

5. R Vmax Voltage imax A Current V a.c. Source Pure Resistance in AC Circuits Voltage and current are in phase, and Ohm’s law applies for effective currents and voltages. Ohm’s law: Veff = ieffR

6. Inductor i i I Inductor I Current Rise 0.63I Current Decay 0.37I t Time, t t Time, t AC and Inductors : The voltage V peaks first, causing rapid rise in icurrent which then peaks as the emf goes to zero. Voltage leads (peaks before) the current by 900. Voltage and current are out of phase.

7. Vmax Voltage imax Current A V L a.c. A Pure Inductor in AC Circuit The voltage peaks 900 before the current peaks. One builds as the other falls and vice versa. The reactancemay be defined as the non-resistiveopposition to the flow of ac current.

8. A V L a.c. Inductive Reactance The back emfinduced by a changing current provides opposition to current, called inductivereactance XL. Such losses are temporary, however, since the current changes direction, periodically re-supplying energy so that no net power is lost in one cycle. Inductive reactance XLis a function of both the inductance and the frequency of the ac current.

9. Inductive Reactance: A V L a.c. Calculating Inductive Reactance The voltage reading V in the above circuit at the instant the ac current is ican be found from the inductance in H and the frequency in Hz. Ohm’s law: VL = ieffXL

10. q Qmax Capacitor Capacitor i Rise in Charge I 0.37 I Current Decay Time, t t 0.63 I Time, t t AC and Capacitance The voltage V peaks ¼ of a cycle after the current ireaches its maximum. The voltage lags the current. Current i and V out of phase.

11. C Vmax Voltage imax A Current V a.c. A Pure Capacitor in AC Circuit The voltage peaks 900 afterthe current peaks. One builds as the other falls and vice versa. The diminishing current i builds charge on C which increases the back emfof VC.

12. C A V a.c. Capacitive Reactance Energy gains and losses are also temporary for capacitors due to the constantly changing ac current. No net power is lost in a complete cycle, even though the capacitor does provide non-resistive opposition (reactance) to the flow of ac current. Capacitive reactance XCis affected by both the capacitance and the frequency of the ac current.

13. Capacitive Reactance: C A V a.c. Calculating capacitive Reactance The voltage reading V in the above circuit at the instant the ac current is ican be found from the inductance in F and the frequency in Hz. Ohm’s law: VC = ieffXC

14. Inductive reactance XL varies directly with frequency as expected since EµDi/Dt. R, X XL XC Capacitive reactance XCvariesinversely withfsince rapid ac allows little time for charge to build up on capacitors. R f Frequencyand AC Circuits Resistance Ris constant and not affected by f.

15. VT Series ac circuit A a.c. R C L VR VC VL Series LRC Circuits Consider an inductor L, a capacitor C, and a resistor Rall connected in series with an ac source. The instantaneous current and voltages can be measured with meters.

16. V V = Vmax sin q VL q 1800 2700 3600 VR 450 900 1350 VC Phasein a Series AC Circuit The voltage leads current in an inductor and lags current in a capacitor. In phase for resistance R. Rotating phasor diagram generates voltage waves for each element R, L, and C showing phase relations. Current i is always in phase with VR.

17. Phasor Diagram Source voltage VL VT VL - VC q VR VC VR Phasorsand Voltage At time t = 0, suppose we read VL, VR and VCfor an ac series circuit. What is the source voltage VT? We handle phase differences by finding the vector sum of these readings. VT = S Vi. The angle qis the phase angle for the ac circuit.

18. Source voltage VT VL - VC q VR Now recall that: VR = iR; VL = iXL;andVC = iVC Calculating Total Source Voltage Treating as vectors, we find: Substitution into the above voltage equation gives:

19. Impedance Z XL - XC f R Impedance in an AC Circuit Impedance Z is defined: Ohm’s law for ac current and impedance: The impedance is the combined opposition to ac current consisting of both resistance and reactance.

20. XL XL= XC R XC Resonantfr XL = XC Resonant Frequency Becauseinductance causes the voltage to lead the current and capacitancecauses it to lag the current, they tend to cancel each other out. Resonance (Maximum Power) occurs when XL = XC

21. Impedance In terms of ac voltage: Z XL - XC P = iV cos f f In terms of the resistance R: R P lost in R only P = i2R Power in an AC Circuit No power is consumed by inductance or capacitance. Thus power is a function of the component of the impedance along resistance: The fraction Cos fis known as the power factor.

22. Capacitive Reactance: Inductive Reactance: Summary Effective current: ieff = 0.707 imax Effective voltage: Veff = 0.707 Vmax

23. Summary (Cont.)

24. In terms of ac voltage: P = iV cos f In terms of the resistance R: P = i2R Summary (Cont.) Power in AC Circuits:

25. PREPERED BY:- Satani Darshana

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