An Assignment Submitted for the fulfillment Of internal work in the subject Physics of B.Sc.I Semester Second (KINETIC THEORY, THERMODYNAMICS AND ELECTRIC CURRENTS) By G.S.Zine Guide Prof. G.R.Jadhao & Prof. S.S. Nimje Department of Physics JIJAMATA MAHAVIDYALAYA, BULDANA 2013

1. Norton’s Theorem 2. Aim of the experiment 3. Apparatus 4. Theory (Statement, Example, Verification of Norton’s Theorem using the simulator, More about Norton’s Theorem) 5. Experimental Procedure 6. Observation and calculations 7. Result 8. Components 9. Conversion to a Thevenin’s equivalence 10. Queueing Theory

Norton's theorem for linear electrical networks, known in Europe as the Mayer–Norton theorem, states that any collection of voltage sources, current sources, and resistors with two terminals is electrically equivalent to an ideal current source, I, in parallel with a single resistor, R. For single-frequency AC systems the theorem can also be applied to general impedances, not just resistors. The Norton equivalent is used to represent any network of linear sources and impedances, at a given frequency. The circuit consists of an ideal current source in parallel with an ideal impedance (or resistor for non-reactive circuits).

Any black box containing only voltage sources, current sources, and other resistors can be converted to a Norton equivalent circuit, comprising exactly one ideal current source and one resistor.

Norton's theorem is an extension of Thevenin's theorem and was introduced in 1926 separately by two people: Siemens & Halske researcher Hans Ferdinand Mayer (1895–1980) and Bell Labs engineer Edward Lawry Norton (1898–1983). The Norton equivalent circuit is a current source with current I No in parallel with a resistance R No. To find the equivalent, 1. Find the Norton current I No. Calculate the output current, I AB, with a short circuit as the load (meaning 0 resistances between A and B). This is I No. 2. Find the Norton resistance R No. When there are no dependent sources (all current and voltage sources are independent), there are two methods of determining the Norton impedance R No.  Calculate the output voltage, V AB, when in open circuit condition (i.e., no load resistor — meaning infinite load resistance). R No equals this V AB divided by I No. 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 R No.

Verification of Norton’s theorem (To calculate the current flowing through resistance R 3 by Norton’s theorem)

Experimental board of Norton’s theorem, Milometer, resistors, battery, connecting wires etc

Statement: Norton’s theorem states that a network consists of several voltage sources, current source and resistor with two terminals, is electrically equivalent to an ideal current source “I NO ” and a single resistor, R NO. Statement: Norton’s theorem states that a network consists of several voltage sources, current source and resistor with two terminals, is electrically equivalent to an ideal current source “I NO ” and a single resistor, R NO.

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’s equivalent circuit is a current source with current “I NO ” in parallel with a resistance R NO. To find its Norton’s equivalent circuit, 1. Find the Norton current “I NO ”. Calculate the output current, “I AB ”, when a short circuit is the load (meaning 0 resistances between A and B) This is I NO. 2. Find the Norton resistance R NO. When there are no dependent sources (i.e. all current and voltage sources are independent), there are two methods of determining the Norton impedance R NO.  Calculate the output voltage, V AB, when in open circuit condition (i.e. no load resistor – meaning infinite load resistance). R NO equals this V AB divide by I NO. 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 R NO. However, when there are dependent sources the more general method must be used. This method is not shown below in the diagrams.

Consider the above circuit. To find the Norton’s equivalent of the above circuit we firstly have to remove the center 40 Ω load resistance 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 R s is found by calculating the total resistance at the terminals A and B giving us the following circuit. Find the Equivalence Resistance (R s ): 10 Ω Resistor in parallel with the 20 Ω Resistor

Having found both the short circuit current, I s and equivalent internal resistance, R s this then gives the following Norton’s equivalent circuit. Norton’s equivalent circuit:

Ok, so far so good, but we now have to solve with the original 40 Ω 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: Then the current flowing in the 40 Ω load resistor can be found as:

Step 1:- 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. In both the cases the current measured across the resistance should be of the same value.

Norton’s theorem and Thevenin’s theorem are equivalent, and the equivalence leads to source transformation in electrical circuits. For an electric circuit the equivalence is given by, The application of Norton’s theorem is similar to that of Thevenin’s theorem. The main application is nothing but the simplification of electrical circuit by introducing source transformation.