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**Thevenin, Norton and Maximum Power Transfer Theorems**

Chapter 12 Thevenin, Norton and Maximum Power Transfer Theorems

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Thevenin’s Theorem Why Thevenin’s Theorem is useful

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**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.

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**Steps to make a Thevenin Circuit**

Write these on white board

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**Calculating RTHEVENIN (RTH)**

RTH = 5kΩ

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**Calculating VTHEVENIN (VTH)**

VTH = 10V

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**Equivalent Thevenin Circuit**

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

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**Using the Thevenin Theorem**

Determine VTH Solving for VTH 10V 5V VTH = VA – VB = 5V

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**Using the Thevenin Theorem**

Determine RTH

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

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**Turning Figure 12.15C into Figure 12.15D**

10kΩ 9kΩ B A 10kΩ 3kΩ

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**Using the Thevenin Theorem**

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**Final Thevenin Circuit (with load)**

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**One more Thevenin Circuit Problem**

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Random Video of the Day https://www.facebook.com/photo.php?v=

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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.

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**What a Norton Circuit Looks Like**

Resistance Norton Current IN 2mA

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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

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Using Norton Shortcut 2mA

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Norton Example

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**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

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

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**Another Practice Problem**

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

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**Maximum Power Transfer**

See notes

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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

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

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**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:

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

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**A Couple Thoughts From Chapter 13**

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**Resistance Varies on Length, Diameter and Material**

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**Stranded Wire vs. Solid Wire**

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Switches SPST SPDT DPST DPDT

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