THIS BLOG CONTAIN ABOUT THE THEVENIN'S THEOREM and NORTON THEOREM
Norton's Theorem
Norton's Theorem states that it is possible to simplify any linear
circuit, no matter how complex, to an equivalent circuit with just a
single current source and parallel resistance connected to a load. Just
as with Thevenin's Theorem, the qualification of “linear” is identical
to that found in the Superposition Theorem: all underlying equations
must be linear (no exponents or roots).
Contrasting our original example circuit against the Norton equivalent: it looks something like this:
. . . after Norton conversion . . .
Remember that a current source is a component whose job is to
provide a constant amount of current, outputting as much or as little
voltage necessary to maintain that constant current.
As with Thevenin's Theorem, everything in the original circuit except
the load resistance has been reduced to an equivalent circuit that is
simpler to analyze. Also similar to Thevenin's Theorem are the steps
used in Norton's Theorem to calculate the Norton source current (INorton) and Norton resistance (RNorton).
As before, the first step is to identify the load resistance and remove it from the original circuit:
Then, to find the Norton current (for the current source in the Norton
equivalent circuit), place a direct wire (short) connection between the
load points and determine the resultant current. Note that this step is
exactly opposite the respective step in Thevenin's Theorem, where we
replaced the load resistor with a break (open circuit):
With zero voltage dropped between the load resistor connection points, the current through R1 is strictly a function of B1's voltage and R1's resistance: 7 amps (I=E/R). Likewise, the current through R3 is now strictly a function of B2's voltage and R3's
resistance: 7 amps (I=E/R). The total current through the short between
the load connection points is the sum of these two currents: 7 amps + 7
amps = 14 amps. This figure of 14 amps becomes the Norton source
current (INorton) in our equivalent circuit:
Remember, the arrow notation for a current source points in the direction opposite
that of electron flow. Again, apologies for the confusion. For better
or for worse, this is standard electronic symbol notation. Blame Mr.
Franklin again!
To calculate the Norton resistance (RNorton), we do the exact same thing as we did for calculating Thevenin resistance (RThevenin):
take the original circuit (with the load resistor still removed),
remove the power sources (in the same style as we did with the
Superposition Theorem: voltage sources replaced with wires and current
sources replaced with breaks), and figure total resistance from one load
connection point to the other:
Now our Norton equivalent circuit looks like this:
If we re-connect our original load resistance of 2 Ω, we can analyze the Norton circuit as a simple parallel arrangement:
As with the Thevenin equivalent circuit, the only useful information from this analysis is the voltage and current values for R2;
the rest of the information is irrelevant to the original circuit.
However, the same advantages seen with Thevenin's Theorem apply to
Norton's as well: if we wish to analyze load resistor voltage and
current over several different values of load resistance, we can use the
Norton equivalent circuit again and again, applying nothing more
complex than simple parallel circuit analysis to determine what's
happening with each trial load.
Thevenin Theorem
This theorem is very conceptual. If we think deeply about an electrical circuit, we can visualize the statements made in Thevenin theorem. Suppose we have to calculate the electric current
through any particular branch in a circuit. This branch is connected
with rest of the circuits at its two terminal. Due to active sources in
the circuit, there is one electric potential difference between the points where the said branch is connected. The current through the said branch is caused by this electric potential difference that appears across the terminals. So rest of the circuit can be considered as a single voltage source, that's voltage is nothing but the open circuit voltage between the terminals where the said branch is connected and the internal resistance of the source is nothing but the equivalent resistance of the circuit looking back into the terminals where, the branch is connected. So the Thevenin theorem can be stated as follows,
- When a particular branch is removed from a circuit, the open circuit voltage appears across the terminals of the circuit, is Thevenin equivalent voltage and,
- The equivalent resistance of the circuit network looking back into the terminals, is Thevenin equivalent resistance.
- If we replace the rest of the circuit network by a single voltage source , then the voltage of the source would be Thevenin equivalent voltage and internal resistance of the voltage source would be Thevenin equivalent resistance which would be connected in series with the source as shown in the figure below.
To make Thevenin theorem easy to understand, we have shown the circuit below,
Here two resistors R1 and R2 are connected in series and this series combination is connected across one voltage source of emf E with internal resistance Ri as shown. One resistive branch of RL is connected across the resistance R2 as shown. Now we have to calculate the current through RL.
First, we have to remove the resistor RL from the terminals A and B.
Second, we have to calculate the open circuit voltage or Thevenin equivalent voltage VT across the terminals A and B.
The electric current through resistance R2,
Hence voltage appears across the terminals A and B i.e.
Third, for applying Thevenin theorem, we have to determine the Thevenin equivalent electrical resistance of the circuit, and for that; first we have to replace the voltage source from the circuit, leaving behind only its internal resistance Ri.
Now view the circuit inwards from the open terminals A and B. It is
found the circuits now consist of two parallel paths - one consisting of
resistance R2 only and the other consisting of resistance R1 and Ri in series.
Thus the Thevenin equivalent resistance RT is viewed from the open terminals A and B is given as. As per Thevenin theorem, when resistance RL is connected across terminals A and B, the network behaves as a source of voltage VT and internal resistance RT and this is called Thevenin equivalent circuit. The electric current through RL is given as,
Thevenin Equivalent Circuit
Learning
Our topic is all about the Thevenin Theorem and I learn from this topic is the Thevenin's Theorem is a way to reduce a network to an equivalent circuit
composed of a single voltage source, series resistance, and series
load. To get easily the answer of the thevenin theorem is we need to follow the steps on how to solve the problem there are the steps of thevenin theorem (1) Find the Thevenin source voltage by removing the load resistor
from the original circuit and calculating voltage across the open
connection points where the load resistor used to be. (2) Find the Thevenin resistance by removing all power sources in
the original circuit (voltage sources shorted and current sources open)
and calculating total resistance between the open connection points. (3) Draw the Thevenin equivalent circuit, with the Thevenin voltage
source in series with the Thevenin resistance. The load resistor
re-attaches between the two open points of the equivalent circuit. (4) Analyze voltage and current for the load resistor following the rules for series circuits. I learn in Norton Theorem is to Norton's Theorem is a way to reduce a network to an equivalent circuit
composed of a single current source, parallel resistance, and parallel
load. The norton theorem have step to get the problem easily there are the step to determine the norton theorem (1) Find the Norton source current by removing the load resistor
from the original circuit and calculating current through a short (wire)
jumping across the open connection points where the load resistor used
to be. (2) Find the Norton resistance by removing all power sources in the
original circuit (voltage sources shorted and current sources open) and
calculating total resistance between the open connection points. (3) Draw the Norton equivalent circuit, with the Norton current
source in parallel with the Norton resistance. The load resistor
re-attaches between the two open points of the equivalent circuit. (4) Analyze voltage and current for the load resistor following the rules for parallel circuits.
