Fundamentals of Electricity, Magnetism, and Circuits Flashcards
What is the convectional current flow?
It’s the theoretical flow of electrons from the positive terminal to the negative terminal
How does current actually flow?
It flows from the negative terminal to the positive terminal because the electrons are negatively charged
What is a source?
A source is something that delivers electrical power
What is a load?
A load is something that absorbs electrical power
What do the arithmetic signs of + and - represent?
The direction of electrical current
What is the effective value of an ac voltage?
Effective = Peak value / Square root of 2
The effective value is sometimes also called the Root Mean Square value of the voltage
What does the effective value of an ac voltage measure?
It’s a measure of the heating effect compared to that of an equivalent dc voltage
How can we represent phasors?
We have two phasors, the voltage phasor E and the current phasor I. These can be drawn like 2D vectors where their size represents their relative magnitude and the angle between them represents the phase difference between them.
Rotating clockwise tells you the angle that the respective phasor leads the other one by
Why may we see a distortion in a voltage waveshape?
- Magnetic Saturation in the cores of transformers
- Switching action of thyristors
- IGBT’s in electronic drives (Insulated-Gate Bipolar Transistor)
What is a Harmonic?
Any voltage or current whose frequencies are integral multiples of f where f is the lowest frequency of a set of sine waves
What is a sine wave with the lowest possible frequency?
The Fundamental Frequency
What is a square wave composed of?
A fundamental wave and an infinite number of harmonics. The higher harmonics have smaller amplitudes so they are less important. However, the high frequency harmonics produce steep sides and sharp courners
How are harmonics created?
- Nonlinear loads such as electric arcs and saturated magnetic circuits
- Whenever voltages and currents are periodically switched, such as in power electronic circuits
What is Fundamental Power?
The useful power that causes a motor to rotate and an arc furnace to heat up
What is the Harmonic Power?
The harmonic voltage multiplied by the harmonic current
What usually happens to the harmonic power?
Dissipated into heat into the ac circuit as heat, so it doesn’t do useful work
What is the product of a harmonic current and fundamental voltage?
Always 0
What is the energy in an inductor?
W = 1/2 * L * I^2
- W = Energy stored in the coil
- L = Inductance of the coil
- I = Current
What is the energy in a capacitor?
W = 1/2 * C * E^2
- W = Energy stored in the capacitor
- C = Capacitance of the capacitor
- E = Voltage
What is the equation for the magnetic field intensity?
H = U/I
- H = Magnetic Field Intensity
- U = Magnetomotive force acting on the component
- I = Length of the component
What is the eqation of the magnetic flux density?
B = phi / A
- B = Flux Density
- phi = Flux in the component
- A = Cross-section of the component
In a vacuum, what is the relationship between the magnetic flux density and the magnetic field intensity?
B = mew0 * H
- B = Flux Density
- mew0 = Magnetic Constant [4 * pi * 10^-7] N/A^2
- H = Magnetic Field Intensity
Approximately, H = 800000 B
What materials have the same B-H curves as vacuum’s?
Non-Magnetic Materials such as paper, copper, rubber and air
What is the B-H curve for a magnetic material?
B = mew0 * mewT * H
- B = Flux Density
- mew0 = Magnetic Constant [4 * pi * 10^-7] N/A^2
- H = Magnetic Field Intensity
- mewT = Relative Permeability of the material
mewT varies with the flux density in the material
What are the two key points stated in Faraday’s Law of Electromagnetic Induction?
- If the flux linking a loop (or turn) varies as a function of time, a voltage is induced between its terminals
- The value of the induced voltage is proportional to the rate of change of flux
What is the equation for the induced voltage using Faraday’s principles?
E = N * Rate of change of flux linkage
- E = Induced Voltage
- N = Number of turns in the coil
What is the value of the voltage induced in a conductor?
E = Blv
- E = Induced voltage
- B = Flux density
- l = Active length of the conductor in the magnetic field
- v = Relative speed of the conductor
What is the Electromagnetic (Lorentz) force on a conductor?
F = BIl
- F = Force acting on the conductor
- B = Flux density of the field
- I = Current in the conductor
- l = Active length of the conductor
Thie force is greatest when the conductor is perpendicular to the field, and zero when the conductor is parallel
What is the direction of the force acting on a straight conductor?
Whenever a conductor carries a current, it’s surrounded by a magnetic field
The direction of the field depends on the direction of the current
If current flows into the page, then the field acts clockwise
If we create a coil using a magnetic material, with a current source, and flow current through it, we create a magnetic field.
We can then increase the current, which will then cause the values of the flux density (B) and the magnetic field intensity(H).
What happens as we then decrease the current to zero?
We can plot a graph of B on the y axis and H on the x axis to help
The flux density doesn’t follow the original curve, but moves along a curve above the original
As we reduce the magnetic field intensity, the magnetic domains that were lined up under the influence of field H tend to retain their original orientation
This is known as hysteresis
When H is reduced to 0, we can see that substancial flux density remains, which is called residual flux density, or residual induction
How can we remove residual flux?
The current needs to flow in the opposite direction, and then we need to increase H in the opposite direction.
What is the name of the field intensity required to reduce the flux to zero?
Coercive Force
What must happen to reduce the flux density to zero?
We need to furnish energy to overrcome the frictional resistance of the magnetic domains
What type of current is used in transformers?
Alternating Current
What is a hystersis loop?
When we have an alternating current, we have an alternating direction for the magnetic domains.
This then leads to having maximum peak flux densities (+B and -B) and peak magnetic field intensities (+H and -H)
If we plot B as a function of H, we will see a closed curve which is called a hysteresis loop
What is Hysteresis loss?
As the flux moves between the positive and negative maximums, the magnetic material absorbs energy during the cycle. As this happens, the energy will be dissipated by heat
What is the Hysteresis loss equal to?
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The amount of heat released per cycle [J/m^3] is equal to the area [in T-A/m] of the hysteresis loop
How can we reduce Hysteresis loss?
We can select magnetic materials with a narrow hysteresis loop, such as the grain-orientated silicon steel used in the cores of alternating-current transformers
What is an Eddy Current?
Loops of electrical current induced with conductors by a changing magnetic field inside the conductor. These currents come from the principles listed under Faraday’s Laws
How can we reduce the losses from Eddy currents in a stationary iron core?
We can split the core into two along it’s length. We then need to insulate between the two halves. The total losses of the two halves is considerably less than the losses of the whole. We can repeat this process to reduce the losses further.
What is the instantaneous voltage induced relative to the inductance of the circuit?
e = L * (di/dt)
- e = Instantaneous voltage induced in the circuit
- L = Inductance of the circuit
- (di/dt) = Rate of change of the current
How can we find how the current increases and decreases with time for an inductor?
We can use the volt-second method which allows us to create a graph
I at time (Initial time + dt) = Initial Current + di
di = 1/L * (e * dt)
di = 1/L (Volt-seconds across the inductance during the interval dt)
What is Kirchhoff’s Voltage Law?
The sum of the voltages around a closed loop is zero. Thus in a closed circuit, the sum of the voltage rises and drops equal zero
What is Kirchhoff’s Current Law?
The sum of the current that arrive into a point equal the sum of the current that leaves the same point
If we have an impedance of Z, carrying a current of I, what will the magnitude of the voltage E be?
E = IZ
What is the polarity of E when moving across an impedance Z in the same direction as the current flow I?
E is positive
What is the polarity of E when moving across an impedance Z in the opposite direction as the current flow I?
E is negative
What are the three types of Impedance?
- Resistive (R)
- Inductiive (jX)
- Capacitive (-jX)
What must we do first to solve Kirchhoff’s Laws with ac circuits?
We need to convert all resistive elements into either resistive, inductive, capacitive elements, or a combonation of all three
