EIT Review – Electric Circuits Electric circuits are used in the generation, transmission and consumption of electric power and energy. Electric circuits are used in the encoding, decoding, storage, retrieval, transmission and processing of information. EIT_1_29 Page 1
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EIT Review Electric Circuitsjsvoboda/EIT_Review.pdfAn electric circuit is an interconnection of electric circuit elements. (Circuit elements are also called devices or components.)
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EIT Review – Electric Circuits
Electric circuits are used in the generation, transmission and consumption of electric power and energy.
Electric circuits are used in the encoding, decoding, storage, retrieval, transmission and processing of information.
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Interpreting the circuit diagram
An electric circuit is an interconnection of electric circuit elements. (Circuit elements are also called devices or components.)
Each circuit element has at least two terminals, i.e. places where that element can be connected to other circuit elements. (Terminals are sometimes called leads.) The parts of the circuit where terminals are connected together are called nodes. (Nodes are also called vertices.)
This circuit is an interconnection of two terminal elements.
The shape of the element indicates it behavior.
Each element is characterized by a parameter, represented either as a value with units or as a variable.
Each element has two terminals that are connected to nodes of the network. The element is said to be incident to the nodes ate which its terminals are connected.
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Element Equations
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Current and Voltage
Two quantities are identified for each two terminal circuit element: the element current and the element voltage.
Current and voltage each have a direction as well as value. •
Changing the direction corresponds to multiplying the value by –1•
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Voltage and Current Waveforms
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Steady State and Transient Parts of a Complete Response
All of the inputs are constant voltages and currents.
The circuit is at steady state.
All of the voltages and currents are constant functions of time and can be represented using real numbers
DC Circuits:
All of the inputs are sinusoidal voltages and currents having the same frequency.
The circuit is at steady state.
All of the voltages and currents are sinusoidal functions of time at the input frequency and can be represented using complex numbers
AC Circuits:
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The Passive Convention
When the reference direction of a particular current points from the + toward the of the polarity of a particular voltage, that current and voltage are said to adhere to the passive convention.
ia and va adhere to the passive convention•
ib and vb adhere to the passive convention•
ia and vb adhere to the passive convention•
ib and va adhere to the passive convention•
The “element equations”, e.g. Ohm's law, use the passive convention:
va = R ia and vb = va = R ia
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The Passive Convention
Specification of power and energy use of the passive convention.
power uses the passive convention
supplied bysupplied to
absorbed byreceived bydelivered bydelivered to
NoYesYesYesNoYes
In cases a and b, the element receives 24 W. In cases c and d, the element supplies 24 W.
Power and Energy: andp vi w pdt
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Kirchhoff's Laws
KCL: The algebraic sum of the currents entering any node is zero.
1 2 3 4 4 5 4 5
1 2 3 5
0, 0 ,
0,...
i i i i i i i i
i i i i
KVL: The algebraic sum of the voltages in any loop are zero.
1 4 5 6 2 30, 0,...v v v v v v
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Informal Analysis of DC circuits
Problem Determine the voltage and current of each of the circuit elements in this circuit.
Solution We can label the circuit as follows:
Apply KCL at the top right node to get
4 40.25 0.75 0 1.0 Ai i
Next, apply KCL at the bottom right node to get
3 4 0.25 1.0 0.25 0.75 Ai i
Next, apply KVL to the loop consisting of the voltage source and the 60 W resistor to get
2 215 0 15 Vv v
Apply Ohm’s law to each of the resistors to get
2
2 3 3
150.25 A, 10 10 0.75 7.5 V,
60 60
vi v i
3 310 10 0.75 7.5 Vv i
and
4 420 20 1 20 Vv i
Next, apply KCL at the bottom left node to get
1 3 2 0.75 0.25 1.0 Ai i i
Next, apply KVL to the loop consisting of the 0.75 A current source and three resistors to get
6 4 3 2 20 ( 7.5) 15 12.5 Vv v v v
Finally, apply KVL to the loop consisting of the 0.25 A current source and the 20 W resistor to get
5 4 20 20 Vv v
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Informal Analysis of DC circuits
Problem Determine the voltage and current of each of the circuit elements in this circuit.
Solution We can label the circuit as follows:
Apply KCL at the top right node to get
4 40.25 0.75 0 1.0 Ai i
Next, apply KCL at the bottom right node to get
3 4 0.25 1.0 0.25 0.75 Ai i
Next, apply KVL to the loop consisting of the voltage source and the 60 W resistor to get
2 215 0 15 Vv v
Apply Ohm’s law to each of the resistors to get
2
2 3 3
150.25 A, 10 10 0.75 7.5 V,
60 60
vi v i
3 310 10 0.75 7.5 Vv i
and
4 420 20 1 20 Vv i
Next, apply KCL at the bottom left node to get
1 3 2 0.75 0.25 1.0 Ai i i
Next, apply KVL to the loop consisting of the 0.75 A current source and three resistors to get
6 4 3 2 20 ( 7.5) 15 12.5 Vv v v v
Finally, apply KVL to the loop consisting of the 0.25 A current source and the 20 W resistor to get