Inductance, capacitance and resistance

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Barbara Wilkins
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1 Inductance, capacitance and resistance As previously discussed inductors and capacitors create loads on a circuit. This is called reactance. It varies depending on current and frequency. At no frequency, or DC there is no reactance. At low frequency capacitors create the most reactance At high frequency inductors create the most reactance

2 Inductance, capacitance and resistance Since inductive reactance varies with frequency and inductance the formula for this is X l =2πfL where f is frequency and L is Henrys and X l is in Ohms. Ohms law for inductance is the same as that used to combine resistances in series and parallel circuits. An inductor will cause current to lag behind voltage because induced voltage resists current changes.

3 Inductance, capacitance and resistance Since capacitive reactance varies with frequency and capacitance the formula for this is X c =1/(2πfC) where f is frequency and C is Farads and X c is in Ohms. Ohms law for capacitance is inverted from that used to combine resistances in series and parallel circuits. A capacitor will cause voltage to lag behind current because at 0 volts charge the circuit will be at maximum current.

4 Inductance, capacitance and resistance Therefore capacitive and inductive reactance counter, or cancel each other. Their effect on phase counters the other s phase effect. ELI the ICEman E leads I with an L (inductor) I leads E with a C (capacitor)

5 Inductance, capacitance and resistance Since resistance doesn t effect phase the net of the two reactances, with the lessor subtracted from the greater, will act upon total impedance at 90 to resistance. But since reactance is already expressed in the form of Ohms in a purely reactive circuit Ohms laws applies normally for a purely inductive or capacitive circuit.

6 Inductance, capacitance and resistance Since both reactance s cause current to lead or lag by 90 they must be added to resistances using the Pythagorean theorem. C 2 = A 2 + B 2 Z t2 = R 2 + X (c-l or l-c) 2 Z t = the circuits total opposition to current flow. If the circuit has no AC, or inductors and capacitors then Z t = R t

7 Inductance, capacitance and resistance Ohms law works for AC circuits with inductors, capacitors and resistances. Series circuits solve for impedance first, in parallel solve for currents since the V-drop is the same across each leg.

8 Inductance, capacitance and resistance Resonance is when the frequency is such that a capacitor in series with an inductor cancel each other s reactance. Similar resonance in a parallel circuit with an inductor and capacitor will have infinite resistance at a resonant frequency.

9 Inductance, capacitance and resistance Power factor is 100% in DC circuits. It is the ratio of apparent power to true power.

10 Inductance, capacitance and resistance Apparent Power is that derived from measuring voltage and current in an AC circuit and multiplying them. True power is the power actually used by the resistive load and does not contain the power lost to reactance. Power factor = 100 X True Power / Apparent Power

11 Inductance, capacitance and resistance 110V 400hz 270 Ω X l = 2πfL X c = 1/(2πfC) R t = R Z 2 = R t2 + (X c -X l ) 2 I t = E/Z 300µf 31mH

12 Inductance, capacitance and resistance 270 Ω X l = 2πfL X c = 1/(2πfC) R t = R I t = E/Z 300µf 110V 400htz 31mH Z = R X l X c /v(x l2 X c2 +(R X l -R X c ) 2 )

13 Transformers A transformer is a set of two or more inductors in close proximity whose purpose is to exchange voltage for current in an AC circuit. If the voltage or current is incorrect for a given application it can be transformed up or down. The catch is if one goes up, the other must go down. The other catch is this will lose some power within the circuit.

14 Transformers

15 Transformers Essentially one inductive coil will have thicker wire with fewer loops or turns than the other. They can be high current or high voltage coils depending on what they need for output.

16 Transformers

17 Transformers

18 Transformers Generally a step up or step down transformer refers to the voltage being stepped. The unit can include a rectifier to convert the output to DC. It can have multiple coils tapped into at various points internally for a series of different outputs from one unit.

19 Transformers

20 Transformers They can be cooled, often in an oil bath. They are limited by the apparent power being driven through them. Excessive power input or output can overheat them. They can have different cores from iron to air.

21 Transformers

22 Transformers They can fully isolate one part of a circuit from another such that electrons do not actually travel through the transformer. or they can be wired such that the circuit is not isolated. They are very efficient, loosing a little power to heat and hysterisis. But they are inductors so will effect the impedance of the AC circuit.

23 Transformers

24 Transformers

25 Transformers

26 Transformers

27 Transformers

28 Transformers

29 Transformers

30 Transformers

31 Transformers Transformers will cause the voltage of an AC circuit to be 180 out of phase between the primary and secondary windings. This is because the current is 90 out of phase with the primary voltage and the secondary voltage is 90 out of phase with that current. Consequently a circuit with multiple transformers must be designed to accommodate phase effect.

32 Transformers

33 Transformers Another neat feature of transformers is that they use almost no power when idling in an AC circuit. In other words when there is no load on the secondary circuit the counter EMF in the primary cancels out almost all current flow in that winding.

34 Transformers They can be single dual or three phase. Each winding will need a reciprocal winding.

35 Transformers

36 Transformers

37 Transformers Their cores will be laminated to reduce eddy current effects. And they can have a core that moves into and out of the coil. This makes it an adjustable transformer which can be used to tune a circuit. Capacitors can also be made variable for the same reason.

38 Transformers

39 Motors are electronic devices. If it operates by internal combustion it is properly called an engine. Like a generator, the relationship of motion, current flow and direction of the magnetic lines of flux will determine what an electric motor will do.

41 Since the left hand rule for generators defines current flow based upon motion direction a reverse rule, the right hand rule for motors defines the motion direction based upon current flow. Each respective finger remains the same with the index finger defining the lines of flux from north to south, the thumb defines the motion force, and the middle finger points to the direction of current flow.

42 This is because of the original left hand rule which describes the behavior of flux around a current carrying conductor. In this case the lines of force below the conductor are in the same direction and repel, while the lines above are opposite and attract.

43 Since this force applied will vary depending on the direction the conductor travels, and since the direction varies since the conductor is on a rotating armature it would eventually hit neutral force and then begin to reverse force. So, more than one conductor is used, there is a switching commutator, and the armature has a lot of mass to ensure momentum.

45 In some strategies they have more than one brush assembly riding on the commutator. This allows more than one set of conductors to apply torque at the same time, but it will also require a second set of field poles.

46 Motors, like anything, have different phases of operation, and different operating needs to meet each specific application. All will need special attention to start spinning, some make their power through high RPM and low torque, other have a reverse need. Some are also combined with a generator function.

47 Like generators there are permanent magnet and electro magnet motors. Typically permanent mag motors are only used in small unit application. Whereas high load/torque units usually utilize electro magnetic fields. These can also be wired in series or parallel with the armature, or both with a split field.

48 Like generators, motors a have problems with armature reaction. They also generate counter EMF as a result of their motion. This is in fact what limits their maximum speed. As a motor approaches this maximum no load speed it s current flow will reduce to very little.

49 If load is applied, RPM will reduce, current flow will increase attempting to reestablish EMF and counter EMF balance. As load is increased, RPM is decreased, and current is increased.

50 In a series wound motor all the current travels through both the field and armature. This allows for a very high torque at low speeds. This is a good design for high load low speed such as a starter motor. But these don t limit well and will go to very high speed if not loaded. Field windings are heavy with fewer turns.

54 In a parallel, or shunt would motor the field is wound with finer wire since there is no armature in line to provide resistance. Consequently these motors don t start well, but are fairly stable in cruise RPM. These units are often known as constant speed motors, although they do vary RPM slightly due to changes in load.

56 But, they will need some strategy to get started. One is to unload them during start, another is to include a small series field to assist starting, or they may have alternative starting strategies if they are an AC motor.

58 DC motors are easily reversible. Just switch the lead polarity of either the field or the armature. Switching the polarity of both will net the same direction of rotation due to the right hand rule.

60 This is very easy in a permanent magnet motor. One way would be to have two opposite would fields in the motor, picking one for each direction. This is common for things like landing gear or flap motors.

62 Brush, commutator and bearing maintenance is the same as that of a generator. Brush arcing may be more of a problem in motors with a high variability of load. Brush phase is critical to RPM and load due to armature reaction.

63 Some units incorporate the use of magnetic brakes and clutches. This allows for a greater control during either starting or stopping the unit. Can be used to prevent undue binding on the mechanical linkage connected to the motor or may disengage the motor when not needed as in the case of the bendix drive used in starter motors. They may also incorporate speed or thermal limiting devices.

66 Many motors are duty limited. They can produce more heat then they can reject during a given period of operation. Starter motors, and landing gear motors my be an example of this.

67 Not all motors are designed to output rotating motion. Some put out linear motion. The simplest of these is the solenoid which is a coil around a movable core. A spring moves the core one way, and the energized field moves it the other way.

68 Another type does spin, but this spinning drives an internal worm gear which then gives high torque linear motion. This is also a torque increasing gear reduction system which is often used in both linear and rotary motors.

69 Although the previous discussion pertains to both DC and AC motors, the two are very different. The AC motor comes in tow main categories: the induction motor, and the synchronous motor. These can be single, two, or three phase motors. (one could go with more phases but the added complexity would not derive much benefit)

71 In general the advantage of AC is that one can get more power for less weight. The down side is batteries don t do AC without help. They also don t self start as well as DC units with equal torque load. A third type, the universal motor, works on both AC and DC, but these are not efficient, particularly at 400hz

72 In essence the induction motor self induces current in the armature, there are no brushes. This is done by winding the fields with each phase of the AC generator in a staggered manner much like the generator is wound. This causes each respective field generated by the phase current to increase and decrease in a manner that emulates a flow around the field perimeter.

74 This is similar to a row of lights with each bulb sequentially turned on so that it looks like the light moves along the path of bulbs. In truth, there is no flow, each bulb simply turns on and off in phase.

76 The rotor in this motor is a can shape with copper bars running the length connected together at the ends via a ring. As the current changes in the surrounding field it induces current in these copper bars. The resultant flux will cause the bars to try to follow the field until it reaches neutral. As such, higher slip causes more torque.

78 So, as the load is increased, RPM is decreased causing more slip, causing more rotor current, causing more force to catch up with the field.

79 Self starting for AC motors is a challenge, particularly single phase units. They are often coupled with a tickler winding that is wired in series with a large electrolytic capacitor. The capacitor splits the current phase from the normal one causing those windings to pull more at zero to low RPM. A centrifugal switch cuts out this winding.

81 Another strategy is to split the field poles slightly with a magnetically shaded side. This in effect curves the magnetic lines causing them to pull at an angle slightly off from the center of rotation. These units are very low torque starting and have been replaced by the Cap start units.

82 A synchronous motor is one where the AC field is the same as the induction unit, but the armature doesn t self induce. It has DC applied to the rotor so it will stay right in phase with the induction windings since it needs no slip to induce rotor current. Typically uses 3 phase current, with a rectifier to produce the rotor DC.

83 Rotor speed in an AC motor is a function of the AC hz, as well as the current being applied and the load being driven. Like their DC counterparts as the load increases current increases, heat generation increases and melt down will eventually happen.

84 Motors

Table of Contents. Introduction...2 Conductors and Insulators...3 Current, Voltage, and Resistance...6

Table of Contents. Introduction...2 Conductors and Insulators...3 Current, Voltage, and Resistance...6 Table of Contents Introduction...2 Conductors and Insulators...3 Current, Voltage, and Resistance...6 Ohm s Law... 11 DC Circuits... 13 Magnetism...20 Alternating Current...23 Inductance and Capacitance...30