Day 5 - Mesh Analysis

Topics Discussed

On day 5 of the ENGR 44 course, we further discussed the advantages and disadvantages of using nodal analysis when working with a circuit. Additionally, we were introduced to another powerful tool used in circuit analysis known as nodal analysis. To illustrate the advantage of mesh analysis over nodal analysis, we analyzed a circuit in the beginning of class using nodal analysis. After being introduced to mesh analysis, we used the new method on the same problem as earlier (Fig. 1). We also did work with other problems to gain more practice with the new method (Fig. 2). We found that the complexity of the problem greatly decreased and that we could now handle a wider range of circuits.

Fig. 1

Fig. 2

Nodal Analysis Lab

The goal of the nodal analysis lab was to find the voltage across a certain resistor first by means of nodal analysis, and second experimentally by means of actual measurement with a voltmeter. To begin, we drew a diagram of the circuit with which we would deal with and calculated the corresponding voltages across certain elements in the circuit. Due to availability, we changed one of the resistors to a 22k ohm resistor.

After calculating the theoretical voltage across the 22k and 6.8k ohm resistors, we proceeded to create the circuit using a breadboard and Analog Discovery System (Fig. 3). With multiple voltage sources, we were careful to make the circuit run properly.

Fig. 3

We measured the voltages across the resistors and compared them with the theoretical voltages and found that we were less than 1% off for both. (Fig. 4)

Fig. 4

Summary

This lab illustrated the versatility and usefulness of nodal analysis. By analyzing the junction between wires in a circuit, we were able to calculate accurate results for the voltages across multiple elements in our circuit that were within 1% of the actual values measured. This lab verified this powerful method and will allow us to handle more complex problems in the future.