Engneering 2

profileGareth Beckham
Brief2Series-ParallelCircuitsandTheveninsTheorem.pptx

Lab 2: Series-Parallel Circuits and Thevenin’s Theorem

ENGR 2105

Dr. Kory Goldammer

Series vs. Parallel

Series Circuit

Current is the same in all components.

Each Resistor has the same electrons passing through it

Parallel Circuit

Voltage is the same across all branches.

Each Resistor has unique electrons passing through it

Series-Parallel Circuits (1)

Example:

Goal: Calculate the current in the circuit below using

Ohm’s Law: IT = VT / RT

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

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Series-Parallel Circuits (2)

Example:

Goal: Calculate the current in the circuit below using

Ohm’s Law: IT = VT / RT

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

R346=4 Ω +6Ω = 10 Ω

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Series-Parallel Circuits (3)

Example:

Goal: Calculate the current in the circuit below using

Ohm’s Law: IT = VT / RT

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

5

Series-Parallel Circuits (4)

Example:

Goal: Calculate the current in the circuit below using

Ohm’s Law: IT = VT / RT

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

R123456=15 Ω +30Ω +5Ω = 50 Ω

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Real World Example: A Kitchen Toaster

Most toasters heat up by passing a current through a heating element. The resistance of the heating element changes as it gets warmer.

If you were tasked to determine the amount of current as a function of temperature, you would need to do the above analysis many times!

Luckily, there is a way to create a shortcut: Thevenin’s Theorem

Thevenin’s Theorem

Thevenin’s theorem simplifies the process of solving for the unknown values of voltage and current in a network by reducing the network to an equivalent series circuit connected to any pair of network terminals.

Any network with two open terminals can be replaced by a single voltage source (VTH) and a series resistance (RTH) connected to the open terminals. A component can be removed to produce the open terminals.

Thevenin Example

We are going to “Thevenize” the circuit below. The circuit exists to power the 2 Ohm load, designated by RL. Our task is to determine the amount of current, IL, through RL.

Thevenin Example: Step 1

Remove the Load Resistor, and determine the voltage across the gap that is created (i.e. the voltage across R2). This voltage is called the Thevenin Voltage, VTH.

Thevenin Example: Step 2

Remove the voltage source and replace it with a wire. Determine the resistance between Point A and Point B where the load resistor was removed. This is the Thevenin Resistance, RTH.

Thevenin Example: Step 3

Create a new circuit. Between points A and B , place a DC Voltage source with voltage VTH in Series with a resistor of Resistance RTH.

Thevenin Example: Step 4

Place the load between points A and B and solve for the total current.

Thevenin Example: Change the Load Resistance

What if the RL changes from 2 Ω to 10 Ω?

RL = 10 Ω

RL = 10 Ω