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I want to find the Thévenin and Norton equivalents for the circuit below. However I'm new to this and I would really appreciate some help.

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I start with a source transformation and naming all the nodes:

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To find \$R_{Th}\$ we kill all the sources, so we have 3 paralell resistors. $$(\frac{1}{2} + \frac{1}{3} + \frac{1}{6})^{-1}=(\frac{3}{6} + \frac{2}{6} + \frac{1}{6})^{-1}=(\frac{6}{6})^{-1}=1 \Omega$$ Since \$R_{Th} = R_{N}\$ we get: \$R_{Th} = R_{N} = 1 \Omega\$

I'm pretty sure that I did that correctly but finding \$V_{Th}\$ and \$I_{N}\$ is more difficult for me. To my understanding, \$V_{Th}\$ would be equal to \$V_{c}\$ at least if the \$18 V\$ voltage source wasn't there. I can set up an equation using the fact that all currents entering a node must be equal to all currents leaving the node. But I don't know how I would find \$I_1\$, \$I_2\$ and \$I_3\$ in that case. How do I find \$V_{Th}\$ and \$I_{N}\$?

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3 Answers 3

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I would really appreciate some help

Usually, these problems area easier to solve by converting the voltage to a current source: -

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Then, because current sources play no role in the impedance it's easy to see that the Thevenin impedance is the parallel combination of the three resistors (1 Ω).

The total current into the 1 Ω is 5 amps, therefore, the Thevenin voltage is 5 volts.

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After finding the R(thevinen) you can find V(thevinen) by using the superposition theorem. Find the open circuit voltage because of each source saperately and then algebraically add them to find the total voltage at the open circuit.

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First of all you have to choose the part of the network to which you want to replace the Thevenin equivalent circuit and which connects to the rest of the network via two terminals. Once this is done, considering the chosen network, cancels the effect of all the generators present in it, you will obtain a simpler network between the two terminals, the impedance between the two terminals is the Thevenin equivalent impedance. Now move on to calculating the voltage of the Thevenin generator: activate all the generators present in the chosen network and separated from the remaining part. The voltage at the two terminals, not connected to the rest of the network, is the Thevenin generator voltage.

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