NETWORKS LAWS AND
THEOREMS
Prepared by Engr. JP Timola
Reference: Electric Circuit
Analysis by Johnny Tan
KIRCHHOFF’S CURRENT LAW
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Sum of currents entering a node is equal to the sum of current leaving it
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C t t i t b iti
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Currents leaving to be negative
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Algebraic sum of the current entering or leaving is zero
EXAMPLE
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Write the KCL equations on nodes d, f, h and l
KIRCHHOFF’S VOLTAGE LAW
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Sum of the voltage rises around any closed path is equal to the sum of the voltage drops around the same path
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Based on the fact that there cannot be a potential difference at a single node
EXAMPLE
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Write the KVL equations
MAXWELL’S MESH EQUATION
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Mesh
-closed path or loop which will enclose an open space
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U d t used id d ti i th d i d equations when Kirchhoff's Laws are
•
Mesh current will be used instead of branch current

EXAMPLE
•
Write the KVL equations for each mesh
NODAL EQUATIONS
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Similar to Maxwell’s but focuses on currents on a node
THEVENIN’S THEOREM
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A linear network terminating on any two nodes and containing any number of sources can be replaced by a single ideal voltage source in series with an internal resistance
SAMPLE PROBLEM
•
Use Thévenin’s theorem to find the current flowing in the 10 Ω resistor for the circuit shown
NORTON’S THEOREM
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A linear network terminating on any two nodes and containing any number of sources can be replaced by a single ideal current source in parallel with an internal resistance
SAMPLE PROBLEM
•
Use Norton’s theorem to determine the current flowing in the 10 Ω resistance for the circuit shown

SOURCE TRANSFORMATION
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An electrical source can be represented by either it Thevenin’s or
Norton’s equivalent
SUPERPOSITION THEOREM
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States that response of a system to a group of sources applied at the different parts of the system is the algebraic sum of the responses to the individual sources, applied one at a time with the others removed.
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To remove a source, short circuit a voltage source or open-circuit a current source
SAMPLE PROBLEM
•
A circuit containing two sources of e.m.f., each with their internal resistance.
Determine the current in each branch of the network by using the superposition theorem.
SEATWORK
•
Determine I
1 for the network
SEATWORK
•
Find the Thévenin equivalent circuit for the network in the shaded area of the network. Then find the current through R
L for values of 2 , 10 , and 100 .
SEATWORK
•
Find the Norton equivalent circuit for the network in the shaded area.