EXP. NO. 6 - THEVENIN'S AND NORTON'S THEOREMS

PURPOSE:

The objective of this experiment is to study Thevenin's and Norton's theorems and their application in circuit analysis.

GENERAL THEORY:

Introduction

In this experiment we will study two theorems which greatly simplify analysis of many linear circuits. The first of these theorems is named after a French engineer working in telegraphy, M. L. Thevenin. He first published a statement of his theorem in 1883. The second theorem, credited to E. L. Norton, may be considered as a corollary to the Thevenin's theorem. Using Thevenin's theorem it is possible to obtain an equivalent circuit of any linear circuit composed of an independent voltage source in series with a resistor, figure 1. Equivalent circuit obtained using Norton's theorem consists of an independent current source in parallel with a resistor, figure 2.

Thevenin's Model
In the laboratory the Thevenin's model (VTH and RTH) may be obtained by the following steps:

  1. Measure voltage at the open circuited terminals of the network. This voltage is VOC or VTH.
  2. Using a multimeter measure the resistance between terminals of network, after all independent voltage and current sources have been replaced with short-circuits and open-circuits, respectively.

Norton's Model

The following outlines the steps needed for evaluating IN and RN in the laboratory:

  1. Measure current flowing between short circuited terminals of network. This is ISC or IN.
  2. Using a multimeter measure equivalent resistance between terminals of network, after all the independent current and voltage sources have been replaced with open-circuits and short-circuits, respectively.

PRELAB:

  1. Find the Thevenin's and Norton's equivalent circuits of network in figure 3, excluding RL. Add RL= 1.2K and find IL and VL.
  2. Repeat the previous step for circuit of figure 4.
  3. Assume that the T network of figure 5 is in a black box. That is, none of the components can be seen and the only access to the circuit is from the terminals at each end of the circuit. Show how R1, R2, and R3 may be found using an ohmmeter to measure resistances as seen from terminals of the black box. Derive equations for R1, R2, and R3.

Warning: This prelab requires a good deal of time and calculations.

PROCEDURE:

  1. Construct figure 3. Measure IN, VTH, and RTH for your circuit using the steps outlined before.
  2. Use RL = 1.2 K as the load for figure 3. Measure IL and VL.
  3. Replace everything in network of figure 3, except RL, with its Thevenin equivalent and measure IL and VL.
  4. Use the Thevenin equivalent and the following resistive values: 1K, 2.2K, 4K, 6.6K, 10K, as the load resistor, measure the voltage drop across the load resistor. Calculate the power delivered to the load resistance by the formula: P=V2/R
  5. Construct figure 4. Measure IN, VTH, and RTH for your circuit using the steps outlined before.
  6. Use RL = 1.2 K as the load for figure 4. Measure IL and VL.
  7. Replace everything in network of figure 4, except RL, with its Thevenin equivalent and measure IL and VL.
  8. Use the Thevenin equivalent and the following resistive values: 300, 680, 1.3K, 3.3K, 5.6K. as the load resistor, measure the voltage drop across the load resistor. Calculate the power delivered to the load resistance.
  9. Using the method and equations from the prelab. Connect figure 5 using R1=1K, R2=2.2K and R3=5.6K and measure the resistances from the terminals and calculate the values of R1, R2 and R3.

ANALYSIS

  1. Compare in a table the IL and VL for each circuit using both the original and equivalent circuit. Explain any discrepancy, if any.
  2. Compare in a table the power delivered by both circuits to the load resistor. What can you infer from the results? (Hint: Rth is important)