Information about Analysis Of Resistive Circuits
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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.
Two resistive 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.
If
implies 
for all (real) values of 
, then with respect to terminals ab and xy, circuit 1 and circuit 2 are equivalent.
Resistors in series and in parallel
Resistors in series:
Resistors in parallel:
- The above simplified for only two resistors in parallel:
Delta-wye transformation
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The transformation is used to establish equivalence for networks with 3 terminals.
For equivalence, the resistance between any pair of terminals must be the same for both networks.
Delta-to-star transformation equations
Star-to-delta transformation equations
Voltage and current division
Voltage division: Consider n resistors that are connected in series. The voltage
across any resistor 
is
Current division: Consider n resistors that are connected in parallel. The current
through any resistor is
for
Special case: Two resistors in parallel
Source transformation
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If the two networks are equivalent with respect to terminals ab, then V and I must be identical for both networks. Thus
or 
See also: Norton's theorem, Thévenin's theorem
Nodal analysis
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
Mesh — a loop that does not contain an inner loop.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.
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 frequency AC circuits by using phasors represented as complex numbers for voltage and current and using complex impedance in place of resistance. AC circuits involving multiple frequencies can be analysed by transforming to the frequency domain, treating each frequency separately and superimposing the results.See also
- Ohm's law
- Kirchhoff's circuit laws
- Millman's Theorem
- Series and parallel circuits
- Wye-delta transform
Other fundamental engineering topics
- Dynamics
- Thermodynamics
- Fluid dynamics
- Engineering economics
- Heat transfer
- Materials science
- Strength of materials
- Statics
External links
- Circuit Analysis Techniques — includes node/mesh analysis, superposition, and thevenin/norton transformation
- Nodal Analysis of Op Amp Circuits
- Analysis of Resistive Circuits
- Circuit Analysis Related Laws, Examples and Solutions
A resistive circuit is an electrical circuit designed to use resistance as a means of controlling the behavior of the electrical current in the circuit. A light bulb is an example of a useful resistive circuit.
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resistor is a two-terminal electrical or electronic component that resists an electric current by producing a voltage drop between its terminals in accordance with Ohm's law: The electrical resistance
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current source is an electrical or electronic device that delivers or absorbs electric current. Current sources can be theoretical or practical. A current source is the dual of a voltage source.
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A voltage source is any device or system that produces an electromotive force between its terminals OR derives a secondary voltage from a primary source of the electromotive force.
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Direct current (DC or "continuous current") is the constant flow of electric charge. This is typically in a conductor such as a wire, but can also be through semiconductors, insulators, or even through a vacuum as in electron or ion beams.
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DC circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors. In this case, the circuit voltages and currents are constant, i.e., independent of time. More technically, a DC circuit has no memory.
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In circuit analysis a phasor is a vector with constant length (A) and constant phase angle (θ). It is usually represented as a complex exponential, A•e j θ.
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Voltage (sometimes also called electric potential difference or electrical tension) is the potential similarity of electrical potential between two points of an electrical or electronic circuit, expressed in volts.
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.
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Definition
The amount of electric current (measured in amperes) through some surface, e.g...... Click the link for more information.
In electronics, a voltage divider is a simple device designed to create a voltage (Vout) which is proportional to another voltage (Vin).
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current divider rule (or CDR) is used to find the electrical current flowing through an impedance or other circuit when it is connected in parallel with another impedance. It is similar in form to the voltage divider rule.
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Norton's theorem for electrical networks states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R.
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In electrical circuit theory, Thévenin's theorem for linear electrical networks states that any combination of voltage sources, current sources and resistors with two terminals is electrically equivalent to a single voltage source V and a single series resistor R.
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In electrical engineering, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit.
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Not to be confused with Kerckhoffs' principle.
Kirchhoff's 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.
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In electrical engineering, mesh analysis (sometimes referred to as loop analysis) or the mesh current method is a method of circuit analysis that uses simultaneous equations, Kirchhoff's voltage law, and Ohm's law to solve for the voltages and currents at any point in
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A mesh is similar to fabric or a web in that it has many connected or weaved pieces. In clothing, a mesh is often defined as a loosely woven fabric that has a large number of closely-spaced holes, frequently used for modern sports jerseys and other clothing.
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Not to be confused with Kerckhoffs' principle.
Kirchhoff's 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.
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In electrical engineering, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage (potential difference) between "nodes" (points where elements or branches connect) in an electrical circuit.
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In electrical engineering, mesh analysis (sometimes referred to as loop analysis) or the mesh current method is a method of circuit analysis that uses simultaneous equations, Kirchhoff's voltage law, and Ohm's law to solve for the voltages and currents at any point in
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In circuit analysis a phasor is a vector with constant length (A) and constant phase angle (θ). It is usually represented as a complex exponential, A•e j θ.
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In mathematics, a complex number is a number of the form
where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1.
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where a and b are real numbers, and i is the imaginary unit, with the property i ² = −1.
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Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
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Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is proportional to the potential difference (i.e. voltage drop or voltage) across the two points, and inversely proportional to the resistance between them.
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Not to be confused with Kerckhoffs' principle.
Kirchhoff's 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.
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In electrical engineering, Millman's Theorem (or the parallel generator theorem) is a useful method to simplify the solution of a circuit. It is named after Jacob Millman, who proved the theorem.
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series or parallel. These two names describe the method of attaching the components, that is one after the other or next to each other. If two or more circuit components are connected end to end like a daisy chain, it is said they are connected in series.
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In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. The former distinguishes it from kinematics and the latter distinguishes it from statics.
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Thermodynamics (from the Greek θερμη, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is a branch of physics that studies the effects of changes in temperature, pressure, and volume on
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Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of gases in motion) and hydrodynamics (the study of liquids in motion).
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