Calculate the current through 6Ω load resistor using thevenin’s theorem and verify the result with Norton’s theorem. (3 Marks)
Answers
Answer:
In the previous three tutorials we have looked at solving complex electrical circuits using Kirchhoff’s Circuit Laws, Mesh Analysis and finally Nodal Analysis. But there are many more “Circuit Analysis Theorems” available to choose from which can calculate the currents and voltages at any point in a circuit. In this tutorial we will look at one of the more common circuit analysis theorems (next to Kirchhoff´s) that has been developed, Thevenin’s Theorem.
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.
Thevenin’s equivalent circuit
thevenins theorem equivalent circuit
As far as the load resistor RL is concerned, any complex “one-port” network consisting of multiple resistive circuit elements and energy sources can be replaced by one single equivalent resistance Rs and one single equivalent voltage Vs. Rs is the source resistance value looking back into the circuit and Vs is the open circuit voltage at the terminals.
For example, consider the circuit from the previous tutorials.
thevenins resistor network
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
Explanation:
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