The theorems that follow are used to figure unknowns in circuits that are too complex to be solved using just Ohm's Law. They are all consistent with Ohm's Law and in a sense elaborations on it. The circuits often involve more than one power source, and these theorems are tools that can solve them.The theorems below can be followed logically to help with any electrical issue. Much like a Los Angeles bankruptcy lawyer would study bankruptcy and tax codes , an electrician can study and master these theorems to become a better electrician.
Contents Notation Ohm's Law  Kirchhoff's Laws  Thevenin's Theorem  Norton's Theorem  Thevenin and Norton Equivalence  Superposition Theorem  Reciprocity Theorem  Compensation Theorem  Millman's Theorem  Joule's Law  Maximum Power Transfer Theorem  StarDelta Transformation  DeltaStar Transformation Notation
Ohm's Law
Similarly, when a voltage E is applied across an impedance Z, the resulting current I through the impedance is equal to the voltage E divided by the impedance Z.
Similarly, when a current I is passed through an impedance Z, the resulting voltage drop V across the impedance is equal to the current I multiplied by the impedance Z.
Alternatively, using admittance Y which is the reciprocal of impedance Z:
Kirchhoff's LawsAt any instant the sum of all the currents flowing into any circuit node is equal to the sum of all the currents flowing out of that node: SI_{in} = SI_{out}
Similarly, at any instant the algebraic sum of all the currents at any circuit node is zero: Kirchhoff's Voltage Law
Similarly, at any instant the algebraic sum of all the voltages around any closed circuit is zero:
This information courtesy of Integrated Publishing Thevenin's TheoremAny linear voltage network which may be viewed from two terminals can be replaced by a voltagesource equivalent circuit comprising a single voltage source E and a single series impedance Z. The voltage E is the opencircuit voltage between the two terminals and the impedance Z is the impedance of the network viewed from the terminals with all voltage sources replaced by their internal impedances. Thevenin's Theorem says you can simplify any linear circuit, regardless of complexity, to an equivalent circuit with a single voltage source and series resistance connected to a load. As in the Superposition Theorem, it must be linear. In other words, passive components such as resistors, inductors and capacitors are okay. Nonlinear components such as semiconductors, do not fall under this theorem. Norton's TheoremAny linear current network which may be viewed from two terminals can be replaced by a currentsource equivalent circuit comprising a single current source I and a single shunt admittance Y. The current I is the shortcircuit current between the two terminals and the admittance Y is the admittance of the network viewed from the terminals with all current sources replaced by their internal admittances. Norton's Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single current source and parallel resistance connected to a load. Just as with Thevenin's Theorem, the qualification of “linear” is identical to that found in the Superposition Theorem: all underlying equations must be linear (no exponents or roots). Thevenin and Norton EquivalenceV_{oc} = E I_{sc} = E / Z V_{load} = E  I_{load}Z I_{load} = E / (Z + Z_{load})
The open circuit, short circuit and load conditions of the Norton model are: Thevenin model from Norton model
Norton model from Thevenin model
When performing network reduction for a Thevenin or Norton model, note that: Superposition TheoremIn a linear network with multiple voltage sources, the current in any branch is the sum of the currents which would flow in that branch due to each voltage source acting alone with all other voltage sources replaced by their internal impedances. Reciprocity TheoremIf a voltage source E acting in one branch of a network causes a current I to flow in another branch of the network, then the same voltage source E acting in the second branch would cause an identical current I to flow in the first branch. Compensation TheoremIf the impedance Z of a branch in a network in which a current I flows is changed by a finite amount dZ, then the change in the currents in all other branches of the network may be calculated by inserting a voltage source of IdZ into that branch with all other voltage sources replaced by their internal impedances. Millman's Theorem (Parallel Generator Theorem)
If any number of admittances Y_{1}, Y_{2}, Y_{3}, ...
meet at a common point P, and the voltages from another point N to the free ends of these admittances
are E_{1}, E_{2}, E_{3}, ... then the voltage between
points P and N is:
The shortcircuit currents available between points P and N due to each of the voltages E_{1}, E_{2}, E_{3}, ... acting through the respective
admitances Y_{1}, Y_{2}, Y_{3}, ... are E_{1}Y_{1}, E_{2}Y_{2}, E_{3}Y_{3},
... so the voltage between points P and N may be expressed as: Joule's Law
When a current I is passed through a resistance R, the resulting power P
dissipated in the resistance is equal to the square of the current I multiplied by the
resistance R:
By substitution using Ohm's Law for the corresponding voltage drop V (= IR) across the
resistance: Maximum Power Transfer TheoremNote that power is zero for an opencircuit (zero current) and for a shortcircuit (zero voltage). Voltage Source
Under maximum power transfer conditions, the load resistance R_{T}, load voltage V_{T}, load current I_{T} and load power P_{T} are: Current Source
Under maximum power transfer conditions, the load conductance G_{T}, load current I_{T}, load voltage V_{T} and load power P_{T} are: Complex Impedances
When a load impedance Z_{T} (comprising variable resistance R_{T} and
constant reactance X_{T}) is connected to an alternating voltage source E_{S}
with series impedance Z_{S} (comprising resistance R_{S} and reactance X_{S}), maximum power transfer to the load occurs when R_{T} is equal to the
magnitude of the impedance comprising Z_{S} in series with X_{T}:
When a load impedance Z_{T} with variable magnitude and constant phase angle (constant power
factor) is connected to an alternating voltage source E_{S} with series impedance Z_{S}, maximum power transfer to the load occurs when the magnitude of Z_{T}
is equal to the magnitude of Z_{S}: Kennelly's StarDelta TransformationZ_{AB} = Z_{AN} + Z_{BN} + (Z_{AN}Z_{BN} / Z_{CN}) = (Z_{AN}Z_{BN} + Z_{BN}Z_{CN} + Z_{CN}Z_{AN}) / Z_{CN} Z_{BC} = Z_{BN} + Z_{CN} + (Z_{BN}Z_{CN} / Z_{AN}) = (Z_{AN}Z_{BN} + Z_{BN}Z_{CN} + Z_{CN}Z_{AN}) / Z_{AN} Z_{CA} = Z_{CN} + Z_{AN} + (Z_{CN}Z_{AN} / Z_{BN}) = (Z_{AN}Z_{BN} + Z_{BN}Z_{CN} + Z_{CN}Z_{AN}) / Z_{BN}
Similarly, using admittances:
In general terms: Kennelly's DeltaStar TransformationZ_{AN} = Z_{CA}Z_{AB} / (Z_{AB} + Z_{BC} + Z_{CA}) Z_{BN} = Z_{AB}Z_{BC} / (Z_{AB} + Z_{BC} + Z_{CA}) Z_{CN} = Z_{BC}Z_{CA} / (Z_{AB} + Z_{BC} + Z_{CA})
Similarly, using admittances:
In general terms: The above information provided by BOWest Pty Ltd Electrical & Project Engineering
Faraday's Law of Electromagnetic InductionFaraday's law of electromagnetic induction deals with the relationship between changing magnetic flux and induced electromotive force. It states: The magnitude of an electromagnetic force induced in a circuit is proportional to the rate of change of the magnetic flux that cuts across the circuit.The amount of induced voltage is determined by: 1. The amount of magnetic flux The greater the number of magnetic field lines cutting across the conductor, the greater the induced voltage. 2. The rate at which the magnetic field lines cut across the conductor The faster the field lines cut across a conductor, or the conductor cuts across the field lines, the greater the induced voltage.
Lenz's LawThe Russian physicist Heinrich Lenz discovered in 1833 the directional relationships among the forces, voltages, and currents of electromagnetic induction. Lenz's law says: An induced electromotive force generates a current that induces a counter magnetic field that opposes the magnetic field generating the current. Thus, when an external magnetic field approaches a conductor, the current that is produced in the conductor will induce a magnetic field in opposition to the approaching external magnetic field. But when the external magnetic field moves away from the conductor, the induced magnetic field in the conductor reverses direction and opposes the change in the direction of the external magnetic field. 
Here is a selection of the most significant electricians' books available online today, at the best prices around. Clicking on any logo provides access to reviews and ratings by electricians. A good place to start is with the 2008 NEC Handbook, which contains the complete text of the current code plus extensive commentary, diagrams and illustrations. Other books of interest for the electrician are available as well.













































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