Introduction to AC Circuits and Power Calculation with Practical Examples

R.N.G.P.I.T, Bardoli Electrical Engineering Department Subject: BEE Prepared By: Proff. K.C.Shah

CH: Introduction to AC Circuits This Lecture contain Theoretical concept of AC Sinusoidal waveforms with R Load Target audience Beneficial for: Undergraduate and diploma student of all branches for their semester examination. Also helpful for GATE and other competitive exams and Interview.

Introduction R Load Voltage applied to pure R

Introduction R Load Voltage applied to pure R V I

Average Power Wattmeter average power measured V I V I = m m m m cos2 P t 2 2 = = t I sin sin P vi V t m m V I = (1 cos2 m m ) P t 2

V I V I V I = = m m = P VI m m m m cos2 P t 2 2 2 2 2 V I 1 = (1 cos2 d t m m ) P t 2 2 0 Power factor: 2 2 V I = d t t d t m m 1 cos2 P 4 0 0 V I = m m P 2

Example: A 230V , 50Hz is applied consisting of a pure resistor of 25 . Determine: The current flowing through the circuit Power circuit Equation for instantaneous voltage and current across a circuit absorbed by the

Introduction L Load Voltage applied to pure L di = e Ldt e + = V L = di dt 0 V V = V e = t dt m sin di L di = V Ldt

Voltage applied to pure L V = t dt m sin di L V = t dt m sin i L = 0 sin( 90 ) i I t m ( cos V ) t = m i L V = 0 m L sin( 90 ) i t

Voltage applied to pure L = 0 sin( 90 ) i I t m = sin V V t m V I

Average Power in L = P V i 2 V i 1 = ( sin2 d t m m ) P t = sin( ) sin P V t i t 2 2 m m 2 0 = sin cos P V i t t m m Average Power consumed in full cycle is zero V i = m m sin2 P t 2

Example: A 0.0014H chock coil with negligible resistance is connected to a 220V, 50Hz supply. Determine: Inductive reactance of coil The current flowing through the coil Power consumed by the coil Maximum energy stored in the coil

Introduction to capacitor Voltage applied to C

When Capacitor connected to DC DC Voltage applied to C

When Capacitor connected to AC = C V cos i t m = C V q Vm = + sin i t 1/ 2 c = C V Sin t q m dq dt d dt = + sin i I t = = C V sin i i t m 2 m

Voltage applied to pure C = + 0 sin( 90 ) i I t m = sin V V t m I V

Average Power in C = P V i 2 V i 1 = d t m m (sin2 ) P t = + sin( ) sin P V t i t 2 2 m m 2 0 = sin cos P V i t t m m Average Power consumed in full cycle is zero Max Energy: V i = m m sin2 P t 2 1 2 = C V 2 W max m

Example: A 318uF Capacitor with is connected to a 200V, Determine: Capacitive reactance offered by capacitor Maximum and rms current Maximum charged on the capacitor Maximum energy stored in the capacitor 50Hz supply. instantaneous

When R-L Load connected to AC supply VL V I VR = + 2 2 V V V V Z R L = I = + 2 2 ( ) ( ) V IR IX L = + 2 2 ( ) R ( ) Z X L = + 2 2 ( ) R ( ) V I X L

When R-L Load connected to AC supply VL V I VR V V I X I R = tan L R X R = = tan L L Z XL X R = 1 tan L R

V i V i = m m m m cos cos(2 ) P t = sin V V t 2 2 m 2 1 = sin( ) i I t = p d t P m 2 0 P V i = V I = m m cos P 2 2 ( ) = sin( ) sin P V t i t m m = cos P V I rms rms V i = m m cos cos(2 ) P t 2

Q factor of coil It is defined as Xl/R or L/R max enegy stored energy dissipated per cycle = (2 ) Q = cos P V I 1LI 2 (I R) T 2 m R Z = = 2 ( ) P IZ I I R = (2 ) Q 2 L( 2 ) 2 2 I fL = = Q 1 f R 2 (I R)

In a circuit consisting of a resistance of 5000 and an inductance of 1.0H in series, a voltage of 150 V at 400Hz Determine: The magnitude and phase of the current and voltage across the resistance and inductance Calculate the power taken by the supply is applied.

Active, Reactive and Apparent power: VI Cos VI Sin I Cos VI V I Sin I

Apparent Power: The total power that appear to be transfer between the source and load is called Apparent power True Power (Active Power): The Power which is actually consumed in the circuit. cos P V I = VI Cos R Z VI Sin VI = = 2 ( ) P IZ I I R Reactive apparent power which neither consumed nor does any useful work in the circuit is called reactive power. Power: The component of

Voltage applied to pure L = 0 sin( 90 ) i I t m = sin V V t m V I

Power factor: The factor by which apparent power is multiplied to get actual power is called Power Factor. Z XL R R Z R + = cos R = cos 2 2 L R X Z XC R + = cos 2 2 C R X Z R XL-XC = cos + 2 2 ( ) R X X L c

A current i=14.14sin(t-/6) flows in an electric circuit when a voltage of V=141.4 sin t Determine: The power factor of the circuit. Calculate the value of true power, apparent power and reactive power of the circuit Calculate R,Z, Xl is applied to it.

When R-C Load connected to AC supply V Z = I = + 2 2 ( ) R ( ) Z X C I VR = + 2 2 V V V R C V = + 2 2 ( ) ( ) V IR IX VC C = + 2 2 ( ) R ( ) V I X C

I When R-L Load connected to AC supply VR VC V V V I X I R = C tan R R X R = = C C tan Z XC X R = 1 C tan

V i V i = + m m m m cos cos(2 ) P t = sin V V t 2 2 m 2 1 = + sin( ) i I t = p d t P m 2 0 P V i = V I = m m cos P 2 2 ( ) = sin( ) sin P V t i t m m = cos P V I V i ( ) = + m m 2sin sin( ) P t t 2 V i = + m m cos cos(2 ) P t 2

A voltage of 125v at 60Hz is applied across a resistor connected in series with a condenser. The current in the circuit is 2.2 Amp and power loss in the resistor is 96.8 watt and that of condenser Determine: The capacitance is negligible resistance and

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