Blog #35 - Calculating Current Using Norton’s Theorem

As part of my problem series in this video, I will be Calculating Current Using Norton’s Theorem. Once I am finished with this series of problems I will be posting them in my Stan store at this web address…https://stan.store/GVB

Our task is to calculate the value of the current IL through the resistor RL in this DC network…this time using Norton’s theorem.

Norton’s theorem states: Any two-terminal linear dc network can be replaced by an equivalent circuit consisting of a constant-current source IN in parallel with a resistor RN.

When using “Norton’s Theorem”  to find the Norton’s Resistance RN. The network is redrawn with the source of emf replaced by a short circuit. (If a current source is present, it is replaced by an open circuit.) 

The resistance of the redrawn network as seen by looking back into the network from the load terminals is calculated. 

This value is RN, where RN = (50 Ω) + (100 Ω)||(100 Ω) = 100 Ω. A comparison of Thevenin’s Theorem shows that RN = RTh.

When Using “Norton’s Theorem” to find the Norton’s Constant-Current Source IN. Terminals A - B are short circuited…

IN is the short-circuit current between terminals A and B, the total resistance that the 100 V battery voltage sees looking into the circuit is

RTotal = 100 Ω + (100 Ω || 50 Ω) = 1331/3 Ω and ITotal the total current flowing from the hundred volt power supply is…according to Ohm's law is

E/RTotal = (100/1331/3 ) = .75 A

Then from the current-divider rule: IN = (3/4 A)(100)/(100 + 50) = 0.5A.

The Norton equivalent circuit consists of IN in parallel with RN. The load resistor RL is connected across the output terminals of Norton equivalent circuit. From the current-divider rule:

IL = (0.5A)[100/(100 + 50)] = 1/3 A.

This Norton solution solved the same circuit as the Thevenin solution. It is often convenient or necessary to have a voltage source rather than a current source or a current source rather than a voltage source. This slide shows the source conversion equations which indicate that a Thevenin equivalent circuit can be replaced by a Norton equivalent circuit, and vice versa, provided that the following equations are used:

RN = RTh

ETh = (IN)(RTh) = IN RN, and…

IN = ETh /RN = ETh /RTh. The conversion between Thevenin and Norton equivalents is generally known as a source transformation.

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Remember, this video has been brought to you by PSPT, where you will find electrical train training videos when you go to this web address…https://bit.ly/47YB3vh…which will also give you a free copy of my 50 page crib sheets that you can use while viewing any of the courses or just keep handy during your every day work.