This course is about the fundamentals of Electric Circuit Analysis. No other
skill for an Electrical Engineer is more basic than Circuit Analysis. Almost all
other courses rely on the mastery of this co
Kirchhoffs Current and Voltage Laws
Kirchoffs Current Law (KCL).
The sum of currents entering a node is equal to the sum of currents leaving that node.
i1 + i4 = i2 + i3 + i5
Equivalent statement of KCL:
The algebraic sum of currents ente
Circuit Elements and Ohms Law
The voltage v(t ) and the current i (t ) in a resistor R are related by:
v = iR
The above relation is valid only if i(t ) enters the (+) terminal and leaves the (-) terminal.
If i (t ) ent
Series and Parallel Connection of Elements,
Conservation of Power
It is important to understand the meaning of Series and Parallel Connection of
Elements. Many errors in circuit analysis come as a result of not doing so.
Circuit Solution by Circuit Reduction
Sources Connected in Series and in Parallel :
Both circuits are invalid. Why?
Circuit (a) violates KVL ideal voltage sources cannot be combined in parallel
(unless they have the same voltage)
Given an ideal voltage source Vs in series with a resistor Rs .
(can we replace them with)
An ideal current source I s in parallel with a resistor R p ?
Connect the same load resisto
VDR, CDR & Circuit Solution by KVL and KCL
The Voltage Divider Rule (VDR)
The total voltage across the series resistors R1 , R2 , . , RN is V.
vx = iRx = N
Rx = N x
vx = N x
The Superposition Principle:
Consider a multi-input multi-output general circuit.
The inputs S1 , S 2 , S3 , ., S N represent either independent voltage or current sources
The outputs O1 , O2 , O3 , ., OM represent the rema
94 Techniques of Circuit Analysis
' R3 To discuss the more-involved methods of circuit analysis, we must d
a few basic terms. So far, all the circuits presented have been p
circuitsthat is, those circui
crossing branches. A circuit t
a . .
Mesh Analysis with current sources
Mesh Analysis (with Current Sources):
When the circuit contains current sources, the above procedure is modified.
Calculate the mesh currents i1 & i2 & i3
KVL around mesh
Mesh Analysis - Introduction
Definition of Mesh
The circuit contains four windows (meshes).
A mesh is simply a window in an electric circuit
Currents through Elements & Mesh Currents:
The currents ia , ib , ic are currents throu
Nodal Analysis with Voltage Sources
Voltage Source Connected to the Reference Node
This case is illustrated by an example.
Calculate the nodal voltages V1 , V2 , V3 .
Nodes 1 & 2
No voltage sources connected
Nodal Analysis Introduction
Definition of Essential Nodes
The essential nodes of the circuit are labeled
0 , 1 , 2 , 3 , 4
All points that are connected by a short circuit belong to the same essential node.
All points in the lower part o
Thevenin Equivalent Circuits
Thevenin Equivalent Circuit:
Given an electrical circuit
split it into circuits A & B
Call circuit B the load
Notice that circuits A & B are connected by the two terminals a & b
Norton Equivalent Circuits and Maxm. Power
Calculation of TEC (Method 3):
Recall method 1: 1) Find Vth = Voc 2) Find Rth =
The first step in method 3 is the same as in method 1, we first find Vth = Voc .
To find Rth method 3 uses