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# Topic1 - 2-1 AC Circuits and Network Theorems Richard...

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2-1 AC Circuits and Network Theorems Richard Bisinella @ 2000 NETWORK THEOREMS TOPIC 2 Aims: Understand basics of: Voltage Dividers Voltage sources & currents Superposition theorem Thevenin’s theorem Millman’s theorem Maximum power transfer theorem

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2-2 AC Circuits and Network Theorems Richard Bisinella @ 2000 2.1 The voltage divider Voltage divider uses: Drop a voltage Provide a reference voltage Easy to use & calculate Potentiometers Volume controls V R 2 i Figure 2.1.1 Basic Voltage divider this R 1 & R 2 Voltage Source: V 0 Voltage across R 1 : V R1 =I.R 1 (Voltage across R 1 ) Voltage across R2: V R2 =I.R 2 (Voltage across R 2 ) V O =IR 1 +IR 2
2-3 AC Circuits and Network Theorems Richard Bisinella @ 2000 Lets find the voltage across R 2 Kirchoff’s voltage law says the sum of the voltages equals zero. V O -V R1 -V R2 =0 V O = V R1+ V R2 Substitute V R1 & V R2 into above equation V O =I.R 1 + I.R 2 = I(R 1 +R 2 ) Rearrange the previous equation to obtain: 2 1 R R V I O + = Substitute I into V R2 = I.R 2 2 1 2 2 R R R V V O R + = (Voltage across R 1 ) Again V R1 can be found by substituting I into V R1 =I.R 1 2 1 1 1 R R R V V O R + = (Voltage across R 1 )

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2-4 AC Circuits and Network Theorems Richard Bisinella @ 2000 Other combinations for a voltage divider: Z 2 Z 1 V 2 Figure 2.1.2 In the above example, in order to find the Voltage V 2 we need to simplify Z 1 to obtain: 1 14 15 12 1 1 1 - + + = R R R Z Z 2 = R 13 Z 1 Z 2 Figure 2.1.3 Universal Voltage divider: 2 1 2 2 Z Z Z V V + = 2 1 1 1 Z Z Z V V + =
2-5 AC Circuits and Network Theorems Richard Bisinella @ 2000 V 4 V 3 V 2 V 1 V 5 V O R 1 R 5 R 4 R 3 R 2 Figure 2.2.4 Voltage divider Total Resistance: R T = R 1 +R 2 +R 3 + … R N Current Through Circuit: V 1 = V O V 2 = V O (R 2 +R 3 +R 4 +R 5 )/R T V 3 = V O (R 3 +R 4 +R 5 )/R T V 4 = V O (R 4 +R 5 )/R T V 5 = V O R 5 /R T (See the pattern) Example: If R 1 =R 2 =R 3 =R 4 =R 5 and V O =10V V 1 =10V, V 2 =(4/5)*10=8V, V 3 =(3/5)*10=6V V 2 =(2/5)*10=4V, V 1 =(1/5)*10=2V T O R V I =

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2-6 AC Circuits and Network Theorems Richard Bisinella @ 2000 In General: IN T SAMPLED OUT V R R V = R SAMPLED : The total resistance up to the point where you measure: For Example: V 3 = V O (R 3 +R 4 +R 5 )/R T R SAMPLED : = R 3 +R 4 +R 5 Figure 2.1.5 Potentiometer (Pot for short Or Variable resistor) Symbol VR 1 1KÙ R T = R 1 +R 2 R 1 =pR T = R 2 =(1-p)R T p: Is the percentage that the knob is turned, p varies from 0 to 1
2-7 AC Circuits and Network Theorems Richard Bisinella @ 2000 2.2 Voltage and Current sources: Figure 2.2.1 Symbols: Ideal Voltage Source:

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Topic1 - 2-1 AC Circuits and Network Theorems Richard...

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