Purpose

To experimentally verify Kirchhoff's Laws while building further multimeter and protoboarding experience.

To use a power balance as a means of verifying that power is conserved in all circuits.

To experimentally show how circuits may fail under poor design considerations.

Prelab 

1. Calculate the resistance seen by the source in circuit 2.1.

2. Use this equivalent resistance along with various circuit theorems to find the voltage and current for each resistor in the network.

   • Perform the calculation at 5V, and again at 12V for the source.

3. For both cases calculate the power absorbed by each resistor, and the total power supplied by the source.

4. Indicate which resistor (circle/highlight etc...) you feel is most likely to exceed the ¼W rating given by the manufacturer.

Theory

Kirchhoff's laws govern the fundamental behavior of circuits. The two laws are as follows:

[1] Current Law:  For any node, in any circuit, at any point in time; the sum of currents entering and exiting said node is always zero.

[2] Voltage law:  For any loop, in any circuit, at any point in time; the sum of voltages across components is always zero.

These two laws, often abbreviated KCL (in the case of Kirchhoff's Current Law) and KVL (in the case of Kirchhoff's Voltage Law), indicate that both charge, and energy are conserved in a circuit. Nodes cannot generate, consume, store, or radiate charge or energy. 

The following lab will serve to familiarize you with Kirchhoff's Laws. 

Problem

AP Engineering Inc. has received many reports from customers and clients that a product they sell has been malfunctioning. Before continuing production AP Engineering would like to remedy the issue with a design revision. The production line technicians and repair personnel have narrowed the issue to one part of the circuit and have provided the details to the product engineering team.

The problematic circuit acts as part of the power supply for a TV. When the TV is off the circuit runs at 5V, when the TV is powered on it runs at 12V. Customers report that the TV's are failing when turned on after a long period of inactivity.

These circuits are constructed using the same 1% tolerance, ¼W resistors from Lab 1, and the values are given below.

Your group has been tasked to evaluate the circuit and then determine which component may be at fault. 

You will then test the circuit to failure to confirm the issue before deciding on an appropriate remedy.

Results

• Compare the Req  that you calculated to the measured equivalent resistance for the circuit.

• Create a chart based on your theoretical predictions showing resistors 1 through 7 and the power dissipated at both 5V and at 12V with the appropriate cell(s) highlighted to indicate the failed component(s).

• Present your 5V test values (Voltage & Current) for Circuit 2.1 along side your prelab calculations in a chart. Note any major discrepancies.

• Explain your findings and recommendations for a solution to the materials selection department.

Questions

1. Describe what is meant by an essential node and an essential loop. Pictures may be used to aid explanation. 

   • How many unique Ohm's Law, KVL, and KCL equations do you think you could write for this circuit?

2. Explain how the Req of a circuit is a convenient way to quickly check that a circuit is built properly if you know the theoretical equivalent resistance.

3. When resistors are damaged in circuit, they often 'fail open' this means that they act like a very large resistor or a open circuit. 

   • Explain how this may have greater consequences to the rest of the design once a single component fails.