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8/16/2019
Circuits 11
Last Lecture โ Chp. #1
System of Units Basic Electrical Quantities Independent Sources Circuit Analysis
๐ ๐ =๐ ๐(๐)
๐ ๐[A = C/s]
๐ ๐ [J = Nโm]
๐ ๐ =๐ ๐(๐)
๐ ๐[V = J/C]
๐ =๐ ๐
๐ ๐= ๐ โ ๐ [W = J/s]
โข Independent Sources
passive sign convention: positive power is defined as thecurrent i(t) entering the positive reference v(t) of the element
โข Power positive โ power being absorbedโข Power negative โ power being supplied
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Circuits 12
Dependent Source
Generate a voltage or current that is determined by another voltage or current at specified location in the circuit.
Voltage Controlled Voltage Source (VCVS)
Current Controlled Voltage Source (CCVS)
Voltage Controlled Current Source (VCCS)
Current Controlled Current Source (CCCS)
8/16/2019
Circuits 13
Example 1.7
Use Tellegenโs theorem to find the current I0 in the network provided.
โข ๐ท๐ = ๐ โ ๐ฐ๐โข ๐ท๐ = ๐๐ โ โ๐ = โ๐๐๐๐พโข ๐ท๐ = ๐๐ โ โ๐ = โ๐๐๐พโข ๐ท๐ฝ๐บ = ๐ โ โ๐ = โ๐๐๐พโข ๐ท๐ช๐บ = ๐ โ โ๐ = โ๐๐๐พโข ๐ท๐ช๐ช๐ฝ๐บ = ๐๐ฐ๐ โ ๐๐ = ๐๐๐๐พ
๐
๐ต
๐ท๐ = ๐ ๐ท๐ = ๐ โ ๐ฐ๐ = ๐๐พ
โด ๐ฐ๐ = ๐๐จ
8/16/2019
Circuits 14
Resistive Circuits โ Chp. #2
โข Ohmโs Lawโข Kirchhoffโs Current and Voltage Lawโข Basic Circuit Analysisโข Equivalent Resistanceโข Voltage and Current Divisionโข Wye and Delta Resistor Networksโข Circuit Analysis with Dependent Sourcesโข Basic Electrical Quantitiesโข Independent & Dependent Sourcesโข Circuit Analysis
8/16/2019
Circuits 15
Ohmโs Law
States that the voltage across a resistance is directly proportional to the current flowing through it.
A circuit element whose electrical characteristicis primarily resistive is called a resistor (R) .
Symbolresistanceโ Ohms (ฮฉ)
๐ ๐ = ๐น โ ๐ ๐
8/16/2019
Circuits 16
Ohmโs Law
๐น =๐ ๐
๐ ๐
๐ ๐ = ๐ ๐ โ ๐ ๐ = ๐น โ ๐ ๐ ๐ =๐ ๐ ๐
๐น
๐ฎ =๐
๐น=๐ ๐
๐ ๐
โข Resistance [ฮฉ = V/A]
โข Conductance [S = A/V]
โข Power Dissipation [W]
siemens
8/16/2019
Circuits 17
Short Circuit / Open Circuit
variable resistor[potentiometer]
๐ ๐ = ๐น โ ๐ ๐๐ ๐ = ๐น โ ๐ ๐ = ๐
for ๐น โ โfor ๐น โ ๐
๐ ๐ =๐ ๐
๐น= ๐
โด short circuit! โด open circuit!
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Circuits 18
Example 2.1
Determine the current I and the power absorbed by the resistor.
I
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Circuits 19
Example 2.2
Determine the voltage source Vs and the current I in the circuit.
I
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Circuits 110
Example 2.3
Find the value of the voltage source Vs and the power absorbed by theresistance.
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Circuits 111
Example 2.4
Find the value of the resistance R and the voltage across the currentsource Vs.
I
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Circuits 112
Kirchhoff's Law
โข Kirchhoffโs Current Law (KCL)โข Kirchhoffโs Voltage Law (KVL)
Node: a point of connection of two or more circuit elements
Loop: any closed path through the circuit in which no node is encountered more than once
Branch: a portion of the circuit containing a single element and the node at each end of the elements
*assumption โ interconnection is performed by electrical conductors (wires) that have zero resistance
8/16/2019
Circuits 113
Kirchhoff's Current Law
โฆ the algebraic sum of the all the currents entering any node is zero
๐=๐
๐ฒ
๐๐๐๐(๐) = ๐
๐=๐
๐ต
๐๐๐๐(๐) =
๐=๐
๐ด
๐๐๐๐๐(๐)
KCL (1): ๐๐ ๐ โ ๐๐ ๐ โ ๐๐ ๐ = ๐KCL (2): ๐๐ ๐ โ ๐๐ ๐ โ ๐๐ ๐ = ๐KCL (3): ๐๐ ๐ + ๐๐ ๐ โ ๐๐ ๐ โ ๐๐ ๐ = ๐KCL (4): ๐๐ ๐ + ๐๐ ๐ โ ๐๐ ๐ = ๐KCL (5): ๐๐ ๐ + ๐๐ ๐ โ ๐๐ ๐ = ๐
8/16/2019
Circuits 114
Learning Assessment E2.5b
โฆ find I1, and I2 in the circuit provided.
8/16/2019
Circuits 115
Learning Assessment E2.6b
โฆ find Ix in the circuit provided.
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Circuits 116
Kirchhoff's Voltage Law
โฆ the algebraic sum of the voltages around any loop is zero
๐=๐
๐ฒ
๐๐ (๐) = ๐KVL: ๐๐ โ ๐ฝ๐น๐ + ๐ โ ๐ฝ๐น๐ + ๐๐ โ ๐ฝ๐น๐ = ๐
*Adopt a sign convention for the voltages across the elements:
โข Increase in energy level โ positiveโข Decrease in energy level โ negative
๐=๐
๐ต
๐๐โ(๐) =
๐=๐
๐ด
๐๐โ(๐)
8/16/2019
Circuits 117
Example 2.12
โฆ write the KVL equation for: 1) abda2) dbcd3) dabcd