FOWLER CHAPTER 9 LECTURE 9 POWER IN AC CIRCUITS
POWER IN RESISTIVE CIRCUITS, CHAP 9WITH A RESISTIVE LOAD, CURRENT AND VOLTAGE ARE IN PHASE. F.9.1THIS COULD BE AN ELECTRIC HEATER, STOVE, LAMP ETC.
Ac source drives a purely resistive load.
In a purely resistive circuit, all circuit power is dissipated by the resistor(s). Voltage and current are in phase with each other.
V
I
+POWER= (-CURRENT)X(-VOLTAGE)
POWER IN OUT OF PHASE CIRCUITSREACTANCE IS LIKE RESISTANCE IN AC CIRCUITSWHICH INCULDES CAPACITORS AND INDUCTORS.
R
VRIIVP
22
RESISTORS
INDUCTORS
CAPACITORS
WHAT DOES NEGETIVE POWER MEAN?
POWER IS FLOWING BACK FROM THE LOAD TO THE SOURCE. WITH A 90° PHASE SHIFT, NO POWER IS USED BY REACTIVE COMPOENTS,ONLY RESISTANCE USES POWER.
POWER IN RESISTIVE, REACTIVE CIRCUITS CAN BE FOUND FROM,
P =IVCOSØFOR RESISITANCE ONLY CIRCUITS: Ø = 0, SO COS(0°) = 1THEN P= IV(1) =IV
Ø
IT
IR
COSØ =IR/IT
COS IS A MATH FUNCTION THAT CAN VARY FROM 1 TO 0FOR A ANGLE IN DEGREES FROM 0° TO 90°.
THERE IS NO EASY WAY TO CALCULATE POWER WHEN PHASE SHIFTS OCCUR.
WHEN CURRENT AND VOLTAGE ARE OPPOSITE; (Neg. or pos.) voltage times (Neg. or pos.) current = - power
If a sinusoidal voltage is applied to an resistive circuit with a phase angle of 0o, the resulting voltage and current waveforms will look like this
Given that power is the product of voltage and current (p = i v), let’s look at the waveform for power in this circuit.
Current
Current (red)
Current
Current
Voltage (green)
Voltage
VoltageVoltage
Power Power
Power Power
30º
90º60º
(a) No phase shift(b) 30º phase shift
(c) 60º phase shift (d) 90º phase shift
Fig. 9-3 Power in phase-shifted circuits. At 90º of phase shift, the power is zero.
+ +
++
- -
--
TRUE POWERIS THE ACTUAL POWER USED BY THE CIRCUIT.IT IS MEASURED WITH A WATTMETER.
APPARENT POWERPOWER IN A CIRCUIT WHEN VOLTAGE AND POWER ARE MEASURED SEPARATELYIT IS CALCULATED IN UNITS OF VOLTAMPERE. (VA)
PTRUE = IVCOSØPAPPARENT =IV
POWER FACTORIS THE RATIO OF TRUE POWER/APPARENT POWER.WHEN CURRENT AND VOLTAGE ARE IN PHASE THE POWER FACTOR = 1.IF 90° OUT OF PHASE THE POWER FACTOR = 0.POWER FACTOR OF A CIRCUIT CAN VARY BETWEEN O AND 1.
Power Factor (PF)Power factor is defined as the ratio of true power (measured in watts) to apparent power (measured in Volt Amps). It measures how effectively AC power is being used by a device. The difference between true power and apparent power is expressed as the power factor and results from the way true power and apparent power are measured. Ideally we would like to have true power and apparent power equal to one another, which would result in a PF of 1.00 or 100% effective power utilization. AC Volts x AC Amps = VA (Volt Amp) Purely Resistive AC Load: VA = Watts (same as DC circuits)
Inductive/Reactive AC Load: VA x PF = WattsAC Volts x AC Amps x PF = Watts
GROUND
NEUTRAL
LINE 1
LINE 2
LINE 3
PHASE 1 277 V
PHASE 2 277 V
PHASE 3 277 V
277 V
277 V
277 V 480 V
480 V
480 V
3 PHASE 277 V/480V, 4 WIRE WYE SYSTEM
TO 3 PHASE LOADS
UNDER LOAD:LINE AND PHASE CURRENTS ARE NOT EQUAL.SINCE 2 PHASE VOLTAGES ARE SEPARATED BY 120º , THEY CANNOT BE ADDED TOGETHERILINE = 1.732IPHASE
VLINE = 1.732VPHASE
VLINE2 = 1.732(277V) =480 VSINGLE PHASE 277 V ARE CONNECTED BETWEEN THE NEUTRAL AND ANY LINE.SINGLE PHASE480 V CIRCUITS ARE CONNECTED BETWEEN ANY 2 OF THE 3 LINES.3 PHASE 480 V ARE CONNECTED ACROSS 3LINES.
RESISTIVE LOAD
IF WE ADD A REACTIVE ELEMENT (CAPACITOR OR INDUCTOR) TO THIS CIRCUIT, THE PF WOULD BE REDUCED.