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Basic Laws of ElectricCircuit
Zuraida Hanim Binti Zaini
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Basic Laws Overview Ideal sources: series & parallel
Resistance & Ohms Law
Definitions: open circuit, short circuit & conductance
Definitions: nodes, branches & loops Kirchhoffs Law
Voltage dividers & series resistors
Current dividers & parallel resistors
Wye-delta Transformations
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Ideal Voltage Sources: Series
Ideal voltage sources connected in series add
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Ideal Voltage Sources: Parallel
Ideal voltage sources cannotbe connected in parallel
Recall: ideal voltage sources guarantee the voltage between twoterminals is at the specified potential (voltage)
Immovable object meets unstoppable force
In practice, the stronger source would win Could easily cause component failure (smoke)
Ideal sources do not exist
Technically allowed ifV1 = V2, but a bad idea
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Ideal Current Sources: Parallel
Ideal current sources in parallel add
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Resistance
All materials resist the flow of current
Resistance is usually represented by the variableR
Depends on geometry and resistivity of the material
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Ohms Law
As with all circuit elements, we need to know how the current throughand voltage across the device are related
Many materials have a complicated nonlinear relationship (including
light bulbs): v = f (i) Materials with a linearrelationship satisfy Ohms law: v = mi
The slope, m, is equal to the resistance of the element
Ohms Law: v = iR
Sign, , is determined by the passive sign convention (PSC)
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Resistors & Passive Sign Convention
Recall that relationships between current and voltage are signsensitive
Passive Sign Convention: Current enters the positive terminals of an
element If PSC satisfied: v = iR
If PSC not satisfied: v = iR
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Other Equations Derived from Ohms Law
Ohms law implies:
Recallp = vi. Therefore
Resistors cannot produce power Therefore, the power absorbed by a resistor will always be positive
1 = 1 V/A
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Example 1: Ohms Law
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Short Circuit as Voltage Source (0 V)
An ideal voltage source Vs = 0 V is also equivalent to a short circuit
Since v = iR andR = 0, v = 0 regardless ofi
Could draw a source with Vs = 0 V, but is not done in practice
Cannot connect a voltage source to a short circuit Irresistible force meets immovable object
In practice, the wire usually wins and the voltage source melts (if notprotected)
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Open Circuit
An element withR = is called a open circuit
Often just omitted
Could draw a resistor withR = , but is unnecessary and would add
clutter
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Open Circuit as Current Source (0 A)
An ideal current source I = 0 A is also equivalent to an open circuit
Could draw a source with I = 0 A, but is not done in practice
Cannot connect a current source to an open circuit
Irresistible force meets immovable object In practice, you blow the current source (if not protected)
The insulator (air) usually wins. Else, sparks fly
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ECE 1131 Electric Circuits
Semester II 2008-2009
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Conductance
Sometimes conductance is specified instead of resistance
Conductance is a measure of the ability of an element to conductelectric current
Inverse of resistance
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Circuit Building Blocks
Before we can begin analysis, we need a common language ad
framework fro describing circuits
For this course, networks and circuits are the same
Networks are composed of nodes, branches and loops
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Nodes Defined
Example: How many nodes? How many essential nodes?
Node: the point of connection between two or more branches
May include a portion of the circuit (more than a single point) Essential Node: the point of connection between three or more
branches
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Branches Defined
Example: How many branches?
Branch: a single two-terminal element in a circuit
Segments of wire are not counted as elements (or branches) Examples: voltage source, resistor, current source
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Kirchhoffs Current Law
Kirchhoffs Current Law (KCL): the algebraic sum of currentsentering a node (or a closed boundary) is zero
The sum of currents entering a node is equal to the sum of the currentsleaving a node
Common sense:
All of the electrons have to go somewhere
The current that goes in, has to come out some place
Based on law of conservation of charge
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Kirchhoffs Current Law for Boundaries
KCL also applies to closed boundaries forallcircuits
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Example 2: Kirchhoffs Current Law
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Kirchhoffs Voltage Law
Kirchhoffs Voltage Law (KVL): the algebraic sum of voltages
around a closed path (or loop) is zero
Based on the conservation of energy
Analogous idea in hydraulic systems: sum of pressure drops and rises
in any closed path must be equal
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Comments on Ohms Law, KCL and KVL
Much of the circuit analysis that we will do is based on these three laws
These laws alone are sufficient to analyze many circuits
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Example 5: Applying the Basic Laws
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Example 6: Applying the Basic Laws
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Resistive Circuits Overview
Resistors in series
Resistors in parallel
Voltage dividers
Current dividers Wye-Delta transformations
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Resistors in Series
Resistors in series add
Similar to voltage sources
Electrically, there is no difference between the two circuits
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Resistors in Parallel
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Resistors in Parallel
Resistors in parallel have a more complicated relationship
Easier to express in terms of conductance
For two resistors:
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Voltage Divider
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Current Divider
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Example: More than one source
Find I1 and I2
Is1 Is2 VR1 R2
+
I1 I2
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Example: More than one source (Cont.)
Apply KCL at the top node
2121
2121
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RR
V
R
V
R
VIIII
ss
Is1 Is2 VR1 R2
+
I1 I2
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RR
RRIIVss
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ECE 1131 Electric Circuits
Semester II 2008-2009
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Exercise 2.13
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Exercise 2.36 (Current Division)
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Example 1: Resistor Networks
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Resistor Networks: Comments
Knowing the equivalent and parallel equivalents of resistors is not
quite adequate
There are some configurations that require one more tool
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Delta Wye Transformations
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Example 2:
Delta Wye Transformation