## AC Loop Analysis App

What it teaches: This program teaches the loop analysis method of solving AC electric networks. It is very similar to the DC Loop Analysis app except that it uses complex numbers to describe the impedance of inductors, resistors and capacitors; complex numbers in polar form (phasors) to describe voltages and currents; and complex arithmetic to solve the system of equations.

The basic idea of the loop analysis method is that an electric network can be considered to be a set of loops with a current flowing around each loop.  Applying Kirchhoff's Voltage Law around the various loops yields a system of equations whose simultaneous solution is the values of the loop currents. Here is a screen shot: How it works: You draw an electric network by activating various tools on the button bar and then clicking or dragging in the main drawing area in the middle of the screen. Depending on the active button you can draw a loop, generator, inductor, etc., or add, move, delete, change the value, direction, etc. of any element at any time.

As the network takes shape the system of equations for the loop currents and their solutions are immediately updated in the equation and solution area at the bottom of the screen.

If you click on a coefficient in the system of equations the part of the circuit responsible for that coefficient blinks. You can also change the display to show the currents through elements, the voltages across the elements or the power dissipated by the elements. When you are finished you can print a report on the circuit.

Some ideas for teachers:

• If you teach math, this application provides a good example of how complex numbers are used in electrical engineering.

• If you teach electricity, you can quickly show the effect of changing loops, directions, elements, etc.

• You can illustrate the concepts of loops and meshes, series and parallel circuits, maximum power transfer, etc.

• You can set up homework and exam problems.

Where to now?

• Home to the MathOnWeb Software homepage.
• Back to see the other 9 apps in the Technology Suite.
• Download this app and the rest of the Technology Suite.