Review
Kirchhoff’s Laws
Voltage and Current Division
CS 21 - Computer Organization and Assembly Language Programming Lecture 8 Introduction to Electrical Devices and Circuits 2 University of the Philippines - Diliman College of Engineering Department of Computer Science
Review
Kirchhoff’s Laws
Outline
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Kirchhoff’s Laws
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Voltage and Current Division
Voltage and Current Division
Review
Kirchhoff’s Laws
Outline
1
Review
2
Kirchhoff’s Laws
3
Voltage and Current Division
Voltage and Current Division
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Kirchhoff’s Laws
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Charge Current Voltage Resistance Power
Voltage and Current Division
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Kirchhoff’s Laws
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Charge - positive or negative (C)
Voltage and Current Division
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Kirchhoff’s Laws
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Charge - positive or negative (C) Current - flow of charges (A)
Voltage and Current Division
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Kirchhoff’s Laws
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Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V)
Voltage and Current Division
Review
Kirchhoff’s Laws
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Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V) Resistance - opposition to current (Ω)
Voltage and Current Division
Review
Kirchhoff’s Laws
Review
Charge - positive or negative (C) Current - flow of charges (A) Voltage - energy required to ”push charges” (V) Resistance - opposition to current (Ω) Power - rate at which energy is expended (W)
Voltage and Current Division
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Kirchhoff’s Laws
More Review
Ohm’s Law Series Parallel
Voltage and Current Division
Review
Kirchhoff’s Laws
More Review Ohm’s Law: V = IR
Voltage and Current Division
Review
Kirchhoff’s Laws
More Review Ohm’s Law: V = IR Series: same current
Voltage and Current Division
Review
Kirchhoff’s Laws
More Review Ohm’s Law: V = IR Series: same current Parallel: same voltage
Voltage and Current Division
Review
Kirchhoff’s Laws
More Review Ohm’s Law: V = IR Series: same current Parallel: same voltage
Voltage and Current Division
Review
Kirchhoff’s Laws
Outline
1
Review
2
Kirchhoff’s Laws
3
Voltage and Current Division
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Current Law Principle of Conservation of Mass The net sum of the currents entering any node is zero
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Current Law Principle of Conservation of Mass The net sum of the currents entering any node is zero
Path of least resistance: there is larger current in the path that has lower resistance
Review
Kirchhoff’s Laws
Kirchhoff’s Current Law Example
Find the current through RA
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Current Law Example
Find the current through RA
We first compute for the current through the 20Ω resistor
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Current Law Example
Find the current through RA
We first compute for the current through the 20Ω resistor Using Ohm’s Law, I = V/R = 40/20 = 2A
Review
Kirchhoff’s Laws
Kirchhoff’s Current Law Example
Simplifying the circuit, we have
Voltage and Current Division
Review
Kirchhoff’s Laws
Kirchhoff’s Current Law Example
Simplifying the circuit, we have
Using KCL, 2A + IA = 5A + 22A
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Current Law Example
Simplifying the circuit, we have
Using KCL, 2A + IA = 5A + 22A
—>
IA = 25A
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Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Voltage Law
Principle of Conservation of Energy The net sum of voltages around any closed path is zero
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Kirchhoff’s Laws
Kirchhoff’s Voltage Law Example Find vx .
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Voltage Law Example Find vx .
First, let’s assign the positive-negative sides on the circuit elements.
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Voltage Law Example Find vx .
First, let’s assign the positive-negative sides on the circuit elements.
Review
Kirchhoff’s Laws
Kirchhoff’s Voltage Law Example Find vx .
Ohm’s Law at 8Ω resistor: V8 = IR = 2A*8Ω = 16V
Voltage and Current Division
Review
Kirchhoff’s Laws
Kirchhoff’s Voltage Law Example Find vx .
Ohm’s Law at 8Ω resistor: V8 = IR = 2A*8Ω = 16V KVL at first loop (first box): -30 + 16 + V10 = 0 V10 = 14V I10 = V10 /R = 14V/10Ω = 1.4A
Voltage and Current Division
Review
Kirchhoff’s Laws
Kirchhoff’s Voltage Law Example Find vx .
KCL at the node: 2 = 1.4 + I2a —>
I2a = 0.6A
Voltage and Current Division
Review
Kirchhoff’s Laws
Kirchhoff’s Voltage Law Example Find vx .
KCL at the node: 2 = 1.4 + I2a —>
I2a = 0.6A
Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Voltage Law Example Find vx .
KCL at the node: 2 = 1.4 + I2a —>
I2a = 0.6A
Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V KVL at second loop: -14 + 1.2 + V2b = 0
—>
V2b = 12.8V
Review
Kirchhoff’s Laws
Voltage and Current Division
Kirchhoff’s Voltage Law Example Find vx .
KCL at the node: 2 = 1.4 + I2a —>
I2a = 0.6A
Ohm’s Law at R2a (2Ω resistor at top): V2a = I2a *R2a = 0.6A*2Ω = 1.2V KVL at second loop: -14 + 1.2 + V2b = 0
—>
V2b = 12.8V = vx
Review
Kirchhoff’s Laws
Outline
1
Review
2
Kirchhoff’s Laws
3
Voltage and Current Division
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Voltage Division Used to express the voltage across one of several series resistors in terms of the voltage across the platform
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Kirchhoff’s Laws
Voltage and Current Division
Voltage Division
Since the circuit is in series, current is constant
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Kirchhoff’s Laws
Voltage Division
Therefore, the current is:
Voltage and Current Division
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Kirchhoff’s Laws
Voltage Division
Solving for the voltage in Resistor 2:
Voltage and Current Division
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Kirchhoff’s Laws
Voltage Division
And for Resistor 1:
Voltage and Current Division
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Kirchhoff’s Laws
Voltage Division
In general:
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage Division Example
Find vx using voltage division.
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage Division Example
Find vx using voltage division.
First, simplify the circuit Use resistor equivalence for parallel resistors
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage Division Example
Find vx using voltage division.
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Voltage Division Example
Find vx using voltage division.
Then solve for vx using the voltage division formula vx = v (Rx / ÎŁR )
Review
Kirchhoff’s Laws
Voltage and Current Division
Voltage Division Example
Find vx using voltage division.
Then solve for vx using the voltage division formula vx = v (Rx / ΣR ) = 10V (2Ω / 10Ω)
Review
Kirchhoff’s Laws
Voltage and Current Division
Voltage Division Example
Find vx using voltage division.
Then solve for vx using the voltage division formula vx = v (Rx / ΣR ) = 10V (2Ω / 10Ω) = 2V
Review
Kirchhoff’s Laws
Voltage and Current Division
Current Division
For parallel resistors, we use current division instead
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Kirchhoff’s Laws
Voltage and Current Division
Current Division
Remember that voltage is constant in parallel connections
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Kirchhoff’s Laws
Voltage and Current Division
Current Division
Using Ohm’s law and Resistor Equivalence:
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Kirchhoff’s Laws
Voltage and Current Division
Current Division
Therefore, the current passing through Resistor 2 is:
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Kirchhoff’s Laws
Voltage and Current Division
Current Division
And the current passing through Resistor 1 is:
Review
Kirchhoff’s Laws
Current Division
In general:
Voltage and Current Division
Review
Kirchhoff’s Laws
Current Division Example
Find V5 .
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well.
Review
Kirchhoff’s Laws
Voltage and Current Division
Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well. Volt sources in series can be summed up into one.
Review
Kirchhoff’s Laws
Voltage and Current Division
Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well. Volt sources in series can be summed up into one. Consider
Review
Kirchhoff’s Laws
Voltage and Current Division
Volt Sources - Series Just like resistors, volt sources can be reduced to one equivalent source as well. Volt sources in series can be summed up into one. We can add all the volt sources in series (as well as the resistors)
Review
Kirchhoff’s Laws
Current Sources - Parallel
We can also reduce current sources. But they must be in parallel connection instead.
Voltage and Current Division
Review
Kirchhoff’s Laws
Voltage and Current Division
Seatwork: Network Analysis Given that a,b,c = 1Ω, d,e,f,g,h,i = 3Ω and j,k,l = 5Ω And suppose the 30V source supplies 12A Find the following: Va , Vf , Vk , Ib , Ie and Il Find the equivalent resistor as well
Review
Kirchhoff’s Laws
So...
Any questions?
Voltage and Current Division