## Cheat Sheet

# Circuit Analysis For Dummies

When doing circuit analysis, you need to know some essential laws, electrical quantities, relationships, and theorems. Ohm’s law is a key device equation that relates current, voltage, and resistance. Using Kirchhoff’s laws, you can simplify a network of resistors using a single equivalent resistor. You can also do the same type of calculation to obtain the equivalent capacitance and inductance for a network of capacitors or inductors. For more complicated circuits, the node-voltage analysis and mesh current techniques come in handy. And when you want to try different loads for a particular source circuit, you can use the Thévenin or Norton equivalent.

## Three Essential Laws for Working with Circuits

At the most basic level, analyzing circuits involves calculating the current and voltage for a particular device. That’s where device and connection equations come in. Device equations describe the relationship between voltage and current for a specific device. One of the most important device equations is Ohm’s law, which relates current *(I) *and voltage *(V)* using resistance *(R)**,** *where* R *is* *a constant: *V *= *IR *or *I *= *V/R *or *R* = *V/I*.

The two connection equations you need to know are Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL):

**Kirchhoff’s current law:**Sum of incoming currents = Sum of outgoing currents at a node**Kirchhoff’s voltage law:**Sum of voltage rises = Sum of voltage drops around a closed loop

## Electrical Quantities and Units of Measurement

Certain electrical quantities, relationships, and electrical units are critical to know when you’re analyzing and characterizing circuit behavior. The following table can help you keep this information straight.

## Equivalent Resistance, Capacitance, and Inductance

When analyzing circuits, you can simplify networks consisting of only resistors, capacitors, or inductors by replacing them with one equivalent device. The following equations show equivalent series and parallel connections for resistor-only, capacitor-only, and inductor-only combinations.

## Analysis Methods for Complex Circuits

When dealing with complicated circuits, such as circuits with many loops and many nodes, you can use a few tricks to simplify the analysis. The following circuit analysis techniques come in handy when you want to find the voltage or current for a specific device. They’re also useful when you have many devices connected in parallel or in series, devices that form loops, or a number of devices connected to a particular node.

**Node-voltage analysis:***Nodes*are particular points in a circuit. When many devices are connected to a particular point, you can make this node a reference node and think of it as having a voltage of 0 V. You then use it as a reference point to measure voltage for a particular node.With node-voltage analysis, you find unknown node voltages in a circuit using Kirchhoff’s current law. After finding the node voltages, you use current-voltage

*(**i-v**)*relationships such as Ohm’s law to find device currents and use the node voltages to find device voltages.**Mesh-current analysis:**A*mesh*is a loop with no devices enclosed by the loop, where the mesh boundaries are those devices that form the loop.*i*-*v*relationships to find device voltages.**Superposition:**For linear circuits with independent sources, you can use superposition to find the voltage and current output for a particular device. Superposition involves turning on sources one at a time while turning off the other sources. You turn off a current source by replacing it with an open circuit, and you turn off a voltage source by replacing it with a short circuit. To get the total output, you calculate the algebraic sum of individual contributions due to each source.**Thévenin/Norton equivalents:**Circuit analysis can become tedious when you’re trying different loads with the same source circuit. To save yourself some work, replace the source circuit with the Thévenin and Norton equivalents.*(V*_{T}*)*in series with one resistor*(R*_{T}*)**,*and*(I*_{N}*)*in parallel with one resistor*(R*_{N}*)*— see the following figure*.*The equivalent circuits will hold for all loads (including open and short circuit loads) if they have the same voltage and current relationships across the terminals.Finding the Thévenin or Norton equivalent requires calculating the following variables:

*V*_{T}*V*_{OC}*,**I*_{N}*I*_{SC}*,*and*R*=_{T}*R*_{N}*V*_{OC}*/I*_{SC}*T*stands for Thévenin,*OC*stands for an open-circuit load,*N*stands for Norton, and*SC*stands for a short circuit load).