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A resistive circuit is a circuit containing only resistors, ideal current sources, and ideal voltage sources. This means that relationships between current and voltage are linear. If the sources are constant (DC) sources, the result is a DC circuit. The analysis of a circuit refers to the process of solving for the voltages and currents present in the circuit. The solution principles outlined here also apply to phasor analysis of AC circuits. Image File history File links Download high resolution version (1748x2225, 18 KB) Circuit diagram used by w:Analysis of resistive circuits. ...
Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ...
In physics a Phasor describes the phase of a particle in a simple harmonic motion or a wave motion. ...
Two electric circuits are said to be equivalent with respect to a pair of terminals if the voltages across the terminals and currents through the terminals are identical for both networks. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ...
This article may be too technical for most readers to understand. ...
In electricity, current refers to electric current, which is the flow of electric charge. ...
If V2 = V1 implies I2 = I1 for all (real) values of V1, then with respect to terminals ab and xy, circuit 1 and circuit 2 are equivalent.
Resistors in series: Resistor symbols A resistor is a two-terminal electrical or electronic component that passes a current that is proportional to the potential difference between its terminals in accordance with Ohms law. ...
Left: Series / Right: Parallel Arrows indicate direction of current flow. ...
Resistors in parallel:
Special case: Two resistors in parallel:
Delta-wye transformation Main article: Y-delta transform The Y-delta transform (also written Wye-delta transform or Kennellys Delta-Star transformation) or star-mesh transformation is a mathematical technique to simplify analysis of an electrical network. ...
The transformation is used to establish equivalence for networks with 3 terminals.
 Delta and Wye Circuit File links The following pages link to this file: Y-delta transform Analysis of resistive circuits Categories: GFDL images ...
For equivalence, the resistance between any pair of terminals must be the same for both networks.
Delta-to-wye transformation equations
Wye-to-delta transformation equations
Voltage and current division Voltage division: Consider n resistors that are connected in series. The voltage across any resistor Ri is In electronics, a voltage divider or resistor divider is a design technique used to create a voltage (Vout) which is proportional to another voltage (Vin). ...
Current division: Consider n resistors that are connected in parallel. The current Ii through any resistor Ri is Circuits Left: Series | Right: Parallel Arrows indicate direction of current flow. ...
for i = 1,2,...,n.
Special case: Two resistors in parallel
Source transformation
 Image File history File links Source Transformation File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
If the two networks are equivalent with respect to terminals ab, then V and I must be identical for both networks. Thus
- V = RIs or
See also: Norton's theorem, Thevenin's theorem Nortons theorem for electrical networks states that any collection of voltage sources and resistors with two terminals is electrically equivalent to an ideal current source I in parallel with a single resistor R. The theorem can also be applied to general impedances, not just resistors. ...
Thevenins theorem for electrical networks states that any combination of voltage sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R. For single frequency AC systems the theorem can also be applied to general impedances, not just resistors. ...
Nodal analysis, or Node-Voltage analysis, is a method of determining the voltage (potential difference) between nodes (points where elements or branches connect) in an electrical circuit. ...
General procedure 1. Label all nodes in the circuit. Arbitrarily select any node as reference.
2. Define a voltage variable from every remaining node to the reference. These voltage variables must be defined as voltage rises with respect to the reference node.
3. Write a KCL equation for every node except the reference.
4. Solve the resulting system of equations.
Mesh analysis
General procedure Mesh - a loop that does not contain an inner loop. A mesh is similar to fabric or a web in that it has many connected or weaved pieces. ...
1. Count the number of “window panes” in the circuit. Assign a mesh current to each window pane.
2. Write a KVL equation for every mesh whose current is unknown.
3. Solve the resulting equations.
Choice of method Given the choice, which method should be used: nodal analysis or mesh analysis?
Nodal analysis: The number of voltage variables equals number of nodes minus one. Every voltage source connected to the reference node reduces the number of unknowns by one. Nodal analysis, or Node-Voltage analysis, is a method of determining the voltage (potential difference) between nodes (points where elements or branches connect) in an electrical circuit. ...
Mesh analysis: The number of current variables equals the number of meshes. Every current source in a mesh reduces the number of unknowns by one.
There is also another point to consider: mesh analysis only applies to planar circuits, i.e. circuits that can be drawn using only two dimensions. Intuitively, what this means is that the wires in the circuit diagram must not "jump over" one another if one is to apply mesh analysis. Nodal analysis, on the other hand, can be applied to both planar and non-planar circuits. Note that sometimes, a circuit that is drawn in a non-planar fashion (i.e. with wires jumping over each other) may be redrawn in planar form, although this is not always the case. Generally, most of the circuits one encounters in elementary resistive network analysis are planar in nature.
To summarize, for planar circuits, either nodal or mesh analysis may be used; generally, the method with the least unknowns to solve for is selected. For circuits that are non-planar, one can try to redraw the circuit in planar form; if this is not possible, one has no choice but to apply nodal analysis.
AC circuits All the techniques given above can be applied to single freqency AC circuits by using phasors represented as complex numbers for voltage and current and using complex impedance in place of resistance. AC cuircuits involving multiple frequencies can be analysed by transforming to the frequency domain, treating each frequency seperately and superimposing the results. A Phasor is a complex number representing a sinusoidal quantity, usually in exponential form. ...
In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ...
In electrical engineering, Impedance is a measure of opposition to a sinusoidal electric current. ...
See also Ohms law, named after its discoverer Georg Ohm [1], states that the potential difference or Voltage drop V between the ends of a conductor (for example, a resistor R) and the current, (I) flowing through R are proportional at a given temperature: where V is the voltage and I...
Kirchhoffs circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. ...
Jacob Millman was born in Russia in 1911. ...
Left: Series / Right: Parallel Arrows indicate direction of current flow. ...
The Y-delta transform (also written Wye-delta transform or Kennellys Delta-Star transformation) or star-mesh transformation is a technique to simplify analysis of an electrical network. ...
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