Norton's Theorem Poker

Posted on

Now we will study theorems which help to determine parameters of only a part of an electric circuit, for example current, voltage and power of a load resistor. These theorems allow replacement of the rest of a circuit as an equivalent source, what facilitates the task of a circuit analysis.

  1. Norton's Theorem Poker Rules
  2. Norton's Theorem Poker Practice
  3. Norton's Theorem Poker Game
  4. Norton S Theorem Procedure
  5. Norton's Theorem Poker Games
  6. Norton S Theorem Problems

Norton’s Theorem is a network reduction electrical network analysis technique which can be used to analyse the current through a branch in complex network of linear electronic components.

Norton’s theorem is another useful tool to analyze electric circuits like using the Thevenin’s Theorem, which reduces linear, active circuits and complex networks into a simple equivalent circuit. A)-Nortan theorem is not applicable to the circuits consists of unilateral elements or non linear elements b)-not applicable to the circuits consists of load in series or parallel with controlled or dependent sources. C)- not applicable to the cir. 4.7 Thevenin’s Theorem In high school, one finds the equivalent resistance of a two terminal resistive circuit without sources. Now, we will find the equivalent circuit for two terminal resistive circuit with sources. Pan 18 4.7 Thevenin’s Theorem Thevenin’s theorem states that a linear two-terminal. Compared to Fundamental Theorem of Arithmetic and Fundamental Theorem of Algebra, Norton wrote: 'the space on which the dynamics take place, can be decomposed uniquely into its basic dynamical parts: points whose dynamics can be described as exhibiting a particular type of recurrence, and points which proceed in a gradient-like fashion.'

Thevenin’s theorem states that we can replace all the electric circuit, except a load resistor, as an independent voltage source in series, and the load resistor response will be the same. The Norton’s theorem states that we can replace the electric circuit except the load resistor as a current source in parallel.

It’s evident that the main use of these theorems is as a replacement of a part of a circuit to simplify the network and get rid of the part of the network which is not useful.

Let us consider the circuit in Figure 29. It’s separated on two parts – circuit with resistor RL, and circuit A, which can be simplified by making source transformations.

Norton's Theorem Poker Rules

Let us make the following transformations – voltage source and 3Ohm resistor can be replaced as 3Ohm resistor and 4A current source in parallel. Parallel resistances will be transformed into 2Ohm resistance, and finally we can transform 4A current source and 2Ohm resistor into a resistor and voltage source in series. From the point of view of RL, the circuit did not change. However, it became simpler. This example lead us to the Thevenin’s Theorem:

As far as a load is concerned, any network composed of ideal voltage and current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal voltage source, in series with an equivalent resistance.

The Norton theorem states the following:

As far as a load is concerned, any network composed of ideal voltage and current sources, and of linear resistors, may be represented by an equivalent circuit consisting of an ideal current source, in parallel with an equivalent resistance.

Construct an electric circuit with passive components and verify Norton's theorem.

Resistors, Battery, connection wire etc..

Norton's theorem states that a network consists of several voltage sources, current sources and resistors with two terminals, is electrically equivalent to an ideal current source ' INO' and a single parallel resistor, RNO. The theorem can be applied to both A.C and D.C cases. The Norton equivalent of a circuit consists of an ideal current source in parallel with an ideal impedance (or resistor for non-reactive circuits).

The Norton equivalent circuit is a current source with current 'INO' in parallel with a resistance RNO.To find its Norton equivalent circuit,

  1. Find the Norton current 'INO'. Calculate the output current, 'IAB', when a short circuit is the load (meaning 0 resistances between A and B). This is INo.
  2. Find the Norton resistance RNo. When there are no dependent sources (i.e., all current and voltage sources are independent), there are two methods of determining the Norton impedance RNo.
  • Calculate the output voltage, VAB, when in open circuit condition (i.e., no load resistor — meaning infinite load resistance). RNo equals this VAB divided by INo.
    or
  • Replace independent voltage sources with short circuits and independent current sources with open circuits. The total resistance across the output port is the Norton impedance RNo.
    However, when there are dependent sources the more general method must be used. This method is not shown below in the diagrams.
  • Connect a constant current source at the output terminals of the circuit with a value of 1 Ampere and calculate the voltage at its terminals. The quotient of this voltage divided by the 1 A current is the Norton impedance RNo. This method must be used if the circuit contains dependent sources, but it can be used in all cases even when there are no dependent sources.

Example 1:-

Consider this circuit-

To find the Norton’s 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.

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:

With A-B Shorted :

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.

Find the Equivalent Resistance (Rs):

10Ω Resistor in parallel with the 20Ω Resistor

Having found both the short circuit current, Is and equivalent internal resistance, Rs this then gives us the following Nortons equivalent circuit.

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:

Norton's Theorem Poker Practice

Norton s theorem problems

The voltage across the terminals A and B with the load resistor connected is given as:

Then the current flowing in the 40Ω load resistor can be found as:

Norton's Theorem Poker Game

Verification of Norton’s Theorem using the simulator,
Step1:- Create the actual circuit and measure the current across the load points.

Step 2:- Create the Norton’s equivalent circuit by first creating a current source of required equivalent current in amperes (2 A in this case), and then measure the current across the load using an ammeter.

Norton S Theorem Procedure

In both the cases the current measured across the resistance should be of the same value.

More about Norton's theorem:

1.Norton's theorem and Thevenin's theorem are equivalent,and the equivalence leads to source transformation in electrical circuits.

Norton's Theorem Poker Games

2.For an electric-circuit,the equivalence is given by ,

VTh=INoxRTh

ie Thevenin's volage=Norton's current x Thevenin's resistance

Norton S Theorem Problems

3.The applications of Norton theorem is similar to that of Thevenin's theorem.The main application is nothing but the simplification of electrical circuit by introducing source transoformation.