# Thevenin, Norton and Maximum Power Transfer Theorems

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Thevenin, Norton and Maximum Power Transfer Theorems
Chapter 12 Thevenin, Norton and Maximum Power Transfer Theorems

Thevenin’s Theorem Why Thevenin’s Theorem is useful

What is Thevenin’s Theorem?
Everything in the original circuit, except the load, maybe replaced by an equivalent circuit. The equivalent circuit consists of a series combination of a voltage source and a resistance.

Steps to make a Thevenin Circuit
Write these on white board

Calculating RTHEVENIN (RTH)
RTH = 5kΩ

Calculating VTHEVENIN (VTH)
VTH = 10V

Equivalent Thevenin Circuit
Now you can place any load in the circuit you want and the calculations are EASY! =10kΩ .66mA

Using the Thevenin Theorem
Determine VTH Solving for VTH 10V 5V VTH = VA – VB = 5V

Using the Thevenin Theorem
Determine RTH

Solving for RTH What is the resistance from point a to b?

Turning Figure 12.15C into Figure 12.15D
10kΩ 9kΩ B A 10kΩ 3kΩ

Using the Thevenin Theorem

One more Thevenin Circuit Problem

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Norton’s Theorem Everything in the original circuit, except the load may be replaced by an equivalent circuit. The equivalent circuit consists of a parallel combination of a current source and a resistance.

What a Norton Circuit Looks Like
Resistance Norton Current IN 2mA

Norton Shortcut There are a bunch of rules for how to calculate the Norton Current and Norton Resistance. However, a shortcut is to find the Thevenin Equivalent circuit and then convert it to a Norton

Using Norton Shortcut 2mA

Norton Example

Other Circuit Analysis Techniques
Besides using traditional circuit analysis using Ohm’s Law, or Superposition, Mesh Analysis, Thevenin’s Theorem, and Norton’s Theorem, there are other circuit analysis techniques. A couple include: Nodal Analysis and Millman’s Theorem Do more hw problems from back of chap 12 (9, 10, 11, or 12) if time

Practice Problem In the following circuit solve for VTH, RTH, IN, RN, IL and VL

Another Practice Problem
Solve for VL using traditional Ohm’s Law technique, Mesh Analysis, and Thevenin Analysis

Maximum Power Transfer
See notes

RL (Ω)0 VT (V) I (A) PL(W) Pi (W) PT (W) Eff (%) 20 2000 1 16.7 278.9 1394 1673.4 2 28.6 14.3 409 1022 1431.5 3 37.5 12.5 468.8 781.3 1250.1 4 44.4 11.1 492.8 616.1 1108.9 5 50 10 500 1000 6 54.5 9.1 496 414.1 910.05 7 58.3 8.3 483.9 344.5 828.35 8 61.6 7.7 474.3 296.5 770.75 9 64.3 7.1 465.5 252.1 717.55 66.7 6.7 446.9 224.5 671.35 80 320 400 30 85.7 2.9 248.5 42.05 290.55 40 88.9 2.2 195.6 24.2 219.8 90.9 1.9 172.7 18.05 190.75

What load resistor would you use for the following circuit to have max power transferred?

What load resistor would you use for the following circuit to have max power transferred?
What circuit analysis technique can we use to solve for this? Thevenin’s Theorem. RTH = 5kΩ 5kOhm 4kOhm 6kOhm I’ve checked this technique using Ohm’s law and it works. See following numbers:

What load resistor would you use for the following circuit to have max power transferred?

A Couple Thoughts From Chapter 13

Resistance Varies on Length, Diameter and Material

Stranded Wire vs. Solid Wire

Switches SPST SPDT DPST DPDT