gel104 dc circuits
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GEL104:
PRINCIPLES OF ELECTRICAL ENGINEERING
Dr. Nitin K. GoelDepartment of Electrical Engineering
IIT Ropar
Room No. - 228
Email: nkgoel@iitrpr.ac.in
Web: http://nkgoel.tech.officelive.com
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DC CIRCUITS
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Electrical circuits can get quite complex. But at the simplest
level, you always have the source of electricity (a battery,
etc.), a load (a light bulb, motor, etc.), and two wires to carry
electricity between the battery and the load. Electrons move
from the source, through the load and back to the source.
Electrical Circuits
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DC Circuits
An Ideal DC circuit (Direct Current Circuit) is an electrical circuit that
consists of any combination of constant voltage sources, constant
current sources, and resistors. In this case, the circuit voltages and
currents are constant,
i.e., independent of time.
More technically, a DC circuit has no memory. That is, a particular circuit
voltage or current does not depend on the past value of any circuit
voltage or current. This implies that the system of equations that represent a DC circuit do
not involve integrals or derivatives (no time dependency).
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DC Circuits
If a capacitor and/or inductor is added to a DC circuit, the resulting
circuit is not, strictly speaking, a DC circuit. However, most such
circuits have a DC solution. This solution gives the circuit voltages
and currents when the circuit is in DC steady state.
More technically, such a circuit is represented by a system of
differential equations. The solution to these equations usually
contain a time varying or transient part as well as constant or
steady state part. It is this steady state part that is the DC solution.
There are some circuits that do not have a DC solution. Two simpleexamples are a constant current source connected to a capacitor
and a constant voltage source connected to an inductor.
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DC Circuits
In electronics, it is common to refer to a circuit that is
powered by a DC voltage source such as a battery or
the output of a DC power supply as a DC circuit even
though what is meant is that the circuit is DC powered.
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CIRCUIT PRINCIPLES
Interconnection of several Circuit Elements Electrical Circuit
Circuits of Considerable Complexities Networks
Network Theorems: Circuit Principles that are capable of general
applications in electrical networks.
Linear Networks Combination of components represented by Ideal
R, L and C and Ideal energy sources V and I
Branch: Part of a circuit with two terminals for connection.
Node: Merging point of two or more branches
Loop: A closed path formed by connecting branches
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KCL and KVL
Kirchhoffs Current Law (KCL) and Kirchhoffs Voltage Law (KVL) are
the fundamental laws of circuit analysis.
KCL is the basis of nodal analysis in which the unknowns are the
voltages at each of the nodesof the circuit.
KVL is the basis of mesh analysis in which the unknowns are the
currents flowing in each of the meshesof the circuit.
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KIRCHOFF CURRENT LAW
This fundamental law results from the conservation of charge. It
applies to ajunction or node in a circuit -- a point in the circuit
where charge has several possible paths to travel.
IA is the only current flowing intothe node. However, there arethree paths for current to leave the node, and these current are
represented by IB, IC, and ID.
Once charge has entered into the node, it has no place to go
except to leave (this is known as conservation of charge). Thetotal charge flowing intoa node must be the same as the the
total charge flowing out ofthe node. So,IB + IC + ID = IA
Bringing everything to the left side of the above equation, we get(IB + IC + ID) - IA = 0
Then, the sum of all the currents is zero.
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KIRCHOFF CURRENT LAW
The algebraic sum of all currents
entering a node is zero, or
The sum of currents entering node is
equal to sum of currents leaving node.
=
=
n
j
ji
1
0
Note the convention we have chosen in previous slide:
Current flowing intothe node are taken to be negative,
Currents flowing outofthe node are positive. It should not really matter which you choose to be the positive or
negative current, as long as you stay consistent.
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KIRCHOFF VOLTAGE LAW
- It states that the algebraic sum of the voltages
around a closed loop must be zero at any instant.
0
1
=
=
n
jjv
Here the total voltage around loop 1 should sum to
zero, as does the total voltage in loop2.
Furthermore, the outer loop of the circuit (the pathABCD) should also sum to zero.
We can adopt the convention that potential gains(i.e. going from lower to higher
potential, such as with an EMF source) is taken to be positive. Potential losses(such as across a resistor) will then be negative.
However, as long as you are consistent in doing your problems, you should be able
to choose whichever convention you like.
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NETWORK THEOREMS
AND
ANALYSIS
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LINEAR CIRCUIT
Voltage across a resistor varies proportionally with its current.
A linear circuit consists of linear elements. The passive elements, the dependentsources and the independent sources used in a linear circuit are linear.
Linearity is between the flux linkage and the current
Linearity is between the charge stored and the capacitor voltage
Linearity of Elements
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SUPERPOSITION THEOREM
The superposition theorem is a method of solving circuits, often used in Linear
circuits with more than one EMF source. It uses Kirchhoff's Voltage Law.
Limitations: Applied only to linear effects such as the current response
The strategy used in the Superposition Theorem is to eliminate all but
one source of power within a network at a time, using series/parallel
analysis to determine voltage drops (and/or currents) within the
modified network for each power source separately.
Once voltage drops and/or currents have been determined for each
power source working separately, the values are all superimposed on
top of each other (added algebraically) to find the actual voltagedrops/currents with all sources active.
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There are two guiding properties Linearity (Proportionality)- Effect (y) is directly proportional to
the cause (x) y=f(x)
Additivity
SUPERPOSITION THEOREM
This theorem states that the linear responses in a circuit with
multiple sources can be obtained as the algebraic sum of
responses, due to each of the independent sources acting alone.
If f is linear f(x+dx)=f(x)+f(dx) y+dy
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Example of Superposition Theorem
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+
SUPERPOSITION THEOREM
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An equivalent circuit refers to the simplest form of a
circuit that retains all of the electrical characteristics of
the original (and more complex) circuit.
In its most common form, an equivalent circuit is made
up of linear, passive elements.
Two circuits are equivalent if they present the same V-I
characteristics.
EQUIVALENT CIRCUIT
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PARALLEL DC CIRCUIT
=
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SERIES-PARALLEL DC CIRCUIT
=
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Thevenins Theorem
Any black box containing only voltage sources, currentsources, and other resistors can be converted to aThvenin equivalent circuit, comprising exactly onevoltage source and one resistor.
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In circuit theory, Thvenin's theorem for linear electrical networksstates that any combination of voltage sources, current sources,
and resistors with two terminals is electrically equivalent to a singlevoltage source Vand a single series resistor R.
For single frequency AC systems the theorem can also be applied
to general impedances, not just resistors.
The theorem was first discovered by German scientist Hermann
von Helmholtz in 1853[1], but was then rediscovered in 1883 by
French telegraph engineer Lon Charles Thvenin (18571926).
Thvenin's Theorem
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Calculate the output current, IAB, when the output terminals are
short circuited (load resistance is 0). RTh equals VTh divided by thisIAB.
Calculating the Thvenin equivalent
To calculate the equivalent circuit, the resistance and voltage are
needed, so two equations are required. These two equations areusually obtained by using the following steps:
Calculate the output voltage, VAB, when in open circuit condition
(no load resistormeaning infinite resistance). This is VTh.
The equivalent circuit is a voltage source with voltage VTh inseries with a resistance RTh.
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Example
Step 0: The original circuit Step 1: Calculating the
equivalent output voltage
Step 2: Calculating theequivalent resistance
Step 3: The equivalent circuit
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In the example, calculating the equivalent voltage
(notice that R1 is not taken into consideration, as above calculations are done in anopen circuit condition between A and B, therefore no current flows through this partwhich means there is no current through R
1and therefore no voltage drop along
this part)
Calculating equivalent resistance:
Example (Contd.)
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