# Thevenin's Theorem

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```					Introduction to Circuit Theory
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   Charge is measured in Coulombs (C)
   1 C = 6.24 x 1018 electrons
   Conventional Current flows from positive to
negative
   Electrons actually flow from negative to
positive
   The measure of the rate of electron flow in a
circuit
   Measured in Amperes (A)
 1 mA (milliamp) = 0.001 A
 1 µA (microamp)= 0.001 mA
   Direct Current (DC)
 Flow of electricity (current) in an unchanging
direction
   Alternating Current (AC)
 Current flows in different directions
Image Source: Electronics Demystified
   Opposition that a component of device offers
to the flow of an electric current
   Unit of resistance is Ohm Ω
 1 kilohm (k Ω) = 1000 Ω
 1 megohm (m Ω) = 1,000 k Ω or 1,000,000 Ω
 Good conductors have low resistance
 Good insulators have high resistance
 Assumption in circuit analysis: Resistance of an
ideal resistor is constant and does not vary in time
   Standard unit of EMF is the volt (V)
   Voltage is the measure of work done to move
a charge from one point to another in an
electric field
 1 mV (millivolt) = 0.001 V
 1 µV (microvolt)= 0.001 mV
   Voltage is referred to as “electric potential” or
“electric pressure”
   More voltage in a circuit means more
potential for current
   V = IR               V
   I =V / R
   R =V / I         I       R

   V – Voltage
   I – Current
   R - Resistance
   DC is 10 V and potentiometer is 10 Ω. What is
the current?
   Potentiometer is 100 Ω and current is 10 mA.
What is voltage across the resistance?
    Potentiometer is uncalibrated. Voltmeter
reads 24 V and Ammeter 3A. What is the
resistance?
   Measure in Watts (W)
   P = IV                     V
   P = I 2R
   P = V2 / R             I       R
   Resistance in Series
 Values are added to get total resistance

   Resistance in Parallel
 Overall resistance decreases
 Conductance (S) siemens
▪ G= 1 / R
 Add conductances to get total resistance
   V1 = V2 = V3
   I = I1 + I2 + I3
   1 / Req = 1 /R1 + 1/R2 + 1/R3
   Current Law – Kirchoff’s First Rule
 The total current entering a junction in a circuit
must equal the sum of the currents leaving that
junction
 Principle of conservation of electric charge

I1 = I2 + I3
I2 = I1 – I3
I3 = I1 – I2
   Voltage Law – Kirchoff’s Second Rule
 The directed sum of the emfs (potential
differences) around any closed circuit it zero
 Principle of conservation of energy

-VB + V1 + V2 = 0
-V2 - V3 + V4 = 0
-VB + V1 - V3 + V4 = 0
 It is possible to simplify a linear circuit, no matter
how complex to an equivalent circuit with just a
single voltage source and series resistance
 This is true for circuits with passive components
(resistors, inductors and capacitors)
 Underlying equations are linear (no exponents or
roots)
 Non-linear (opposition to current changes with
voltage/current)
   Useful for analyzing circuits where one
component is changing
   Tedious re-calculation does not need to occur
   Advantage of Thevenin Conversion is a
simpler circuit which makes load voltage and
current easier to solve
   Step 1
 The chosen load resistor is removed from the
original circuit and replaced with a break (open
circuit)
•Next, the voltage between the two points where the load resistor used
to be attached is determined
•Ohm’s and Kirchoff’s voltage law can be used
•The voltage between the two load connection points can be figured
from one of the battery’s voltage and one of the resistor’s voltage drops
   Step 2
 Find the Thevenin series resistance for the circuit
 Remove all power sources from the circuit and
replace them with wires (current sources are
replaced with breaks)
 Total resistance is R1 and R3 in parallel
= 0.8 Ω
   With the 2 load resistor attached between
the points we can determine the voltage
across it
   Just a simple series circuit
1.   Find Thevenin Voltage by removing load
resistor from original circuit and calculate
voltage across open connection points
2.   Find Thev. resistance be removing power
sources from original circuit (voltage
shorted and current sources open) and
calculate total resistance between points
3.   Draw Thev Eq circuit with Thev voltage in
series with Thev resistance and load resistor
   Possible to simplify linear circuit to a circuit
with just a single current source and parallel
   Step 1
 Remove load resistor and place a short connection
 Calculate total current between the load points
   Step 2 – Calculate Norton Resistance in the
same manner as Thev Resistance
1.   Find Norton Current by removing load
resistor from original circuit and calculate
current across closed connection points
2.   Find Norton resistance be removing power
sources from original circuit (voltage
shorted and current sources open) and
calculate total resistance between points
3.   Draw Norton Eq circuit with Norton Current
Source in parallel with Thev resistance and