Expanded Tertiary Education Equivalency and Accreditation Program (Eteeap)
Expanded Tertiary Education Equivalency and Accreditation Program (Eteeap)
Expanded Tertiary Education Equivalency and Accreditation Program (Eteeap)
Research # 3:
Electrical Circuits 1
Submitted to:
Submitted by:
Noel L. Nantes
BSEE - ETEEAP
Date of Submission:
24 November 2019
University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph
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Lucena City, Philippines
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We saw in the Resistors tutorial that a single equivalent resistance, ( RT ) can be found when two
or more resistors are connected together in either series, parallel or combinations of both, and
that these circuits obey Ohm’s Law.
However, sometimes in complex circuits such as bridge or T networks, we can not simply use
Ohm’s Law alone to find the voltages or currents circulating within the circuit. For these types of
calculations we need certain rules which allow us to obtain the circuit equations and for this we
can use Kirchhoffs Circuit Law.
In 1845, a German physicist, Gustav Kirchhoff developed a pair or set of rules or laws which
deal with the conservation of current and energy within electrical circuits. These two rules are
commonly known as: Kirchhoffs Circuit Laws with one of Kirchhoffs laws dealing with the
current flowing around a closed circuit, Kirchhoffs Current Law, (KCL) while the other law
deals with the voltage sources present in a closed circuit, Kirchhoffs Voltage Law, (KVL).
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Kirchhoffs Current Law
CHED CEB Res. 076-2009
Here, the three currents entering the node, I1, I2, I3 are all positive in value and the two currents
leaving the node, I4 and I5 are negative in value. Then this means we can also rewrite the
equation as;
I1 + I2 + I3 – I4 – I5 = 0
The term Node in an electrical circuit generally refers to a connection or junction of two or more
current carrying paths or elements such as cables and components. Also for current to flow either
in or out of a node a closed circuit path must exist. We can use Kirchhoff’s current law when
analysing parallel circuits.
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Starting at any point in the loop continue in the same direction noting the direction of all the
voltage drops, either positive or negative, and returning back to the same starting point. It is
important to maintain the same direction either clockwise or anti-clockwise or the final voltage
sum will not be equal to zero. We can use Kirchhoff’s voltage law when analysing series circuits.
When analysing either DC circuits or AC circuits using Kirchhoffs Circuit Laws a number of
definitions and terminologies are used to describe the parts of the circuit being analysed such as:
node, paths, branches, loops and meshes. These terms are used frequently in circuit analysis so it
is important to understand them.
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A Typical DC Circuit
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Manuel S. Enverga University Foundation
Lucena City, Philippines
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University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph
Manuel S. Enverga University Foundation
Lucena City, Philippines
Granted Autonomous Status
Thevenin’s Theorem
Thevenin theorem is an analytical method used to change a complex circuit into a simple
equivalent circuit consisting of a single resistance in series with a source voltage
Thevenin’s Theorem states that “Any linear circuit containing several voltages and resistances
can be replaced by just one single voltage in series with a single resistance connected across the
load“. In other words, it is possible to simplify any electrical circuit, no matter how complex, to
an equivalent two-terminal circuit with just a single constant voltage source in series with a
resistance (or impedance) connected to a load as shown below.
Thevenin’s Theorem is especially useful in the circuit analysis of power or battery systems and
other interconnected resistive circuits where it will have an effect on the adjoining part of the
circuit.
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Firstly, to analyse the circuit we have to remove the centre 40Ω load resistor connected across
the terminals A-B, and remove any internal resistance associated with the voltage source(s). This
is done by shorting out all the voltage sources connected to the circuit, that is v = 0, or open
circuit any connected current sources making i = 0. The reason for this is that we want to have an
ideal voltage source or an ideal current source for the circuit analysis.
The value of the equivalent resistance, Rs is found by calculating the total resistance looking
back from the terminals A and B with all the voltage sources shorted. We then get the following
circuit.
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The voltage Vs is defined as the total voltage across the terminals A and B when there is an open
circuit between them. That is without the load resistor RL connected.
We now need to reconnect the two voltages back into the circuit, and as VS = VAB the current
flowing around the loop is calculated as:
This current of 0.33 amperes (330mA) is common to both resistors so the voltage drop across
the 20Ω resistor or the 10Ω resistor can be calculated as:
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and from this the current flowing around the circuit is given as:
which again, is the same value of 0.286 amps, we found using Kirchhoff’s circuit law in the
previous circuit analysis tutorial.
Thevenin’s theorem can be used as another type of circuit analysis method and is particularly
useful in the analysis of complicated circuits consisting of one or more voltage or current source
and resistors that are arranged in the usual parallel and series connections.
While Thevenin’s circuit theorem can be described mathematically in terms of current and
voltage, it is not as powerful as Mesh Current Analysis or Nodal Voltage Analysis in larger
networks because the use of Mesh or Nodal analysis is usually necessary in any Thevenin
exercise, so it might as well be used from the start. However, Thevenin’s equivalent circuits of
Transistors, Voltage Sources such as batteries etc, are very useful in circuit design.
University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph
Manuel S. Enverga University Foundation
Lucena City, Philippines
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Nortons Theorem
Nortons theorem is an analytical method used to change a complex circuit into a simple
equivalent circuit consisting of a single resistance in parallel with a current source
Nortons Theorem states that “Any linear circuit containing several energy sources and
resistances can be replaced by a single Constant Current generator in parallel with a Single
Resistor“.
As far as the load resistance, RL is concerned this single resistance, RS is the value of the
resistance looking back into the network with all the current sources open circuited and IS is the
short circuit current at the output terminals as shown below.
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The value of this “constant current” is one which would flow if the two output terminals where
shorted together while the source resistance would be measured looking back into the terminals,
(the same as Thevenin).
For example, consider our now familiar circuit from the previous section.
To find the Nortons equivalent of the above circuit we firstly have to remove the centre 40Ω load
resistor and short out the terminals A and B to give us the following circuit.
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When the terminals A and B are shorted together the two resistors are connected in parallel
across their two respective voltage sources and the currents flowing through each resistor as well
as the total short circuit current can now be calculated as:
If we short-out the two voltage sources and open circuit terminals A and B, the two resistors are
now effectively connected together in parallel. The value of the internal resistor Rs is found by
calculating the total resistance at the terminals A and B giving us the following circuit.
University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph
Manuel S. Enverga University Foundation
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Find the Equivalent Resistance (Rs)
CHED CEB Res. 076-2009
Having found both the short circuit current, Is and equivalent internal resistance, Rs this then
gives us the following Nortons equivalent circuit.
Ok, so far so good, but we now have to solve with the original 40Ω load resistor connected
across terminals A and B as shown below.
Again, the two resistors are connected in parallel across the terminals A and B which gives us a
total resistance of:
The voltage across the terminals A and B with the load resistor connected is given as:
University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph
Manuel S. Enverga University Foundation
Lucena City, Philippines
Granted Autonomous Status
Once again and using Nortons theorem, the value of current for I3 is still calculated
as 0.286 amps, which we found using Kirchhoff´s circuit law in the previous tutorials.
References:
https://www.electronics-tutorials.ws/dccircuits/dcp_4.html
https://www.electronics-tutorials.ws/dccircuits/dcp_7.html
https://www.electronics-tutorials.ws/dccircuits/dcp_8.html
University Site, Red-V, Lucena City, Philippines; Tel No. (042) 373-6067; Fax No. 373-6065 www.mseuf.edu.ph