ainster31
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[Circuits] Finding the Thevenin and Norton Equivalents #2
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Jony130
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Here's a hint that might help.
If you consider a general Thevenin model with a resistive load attached, you've really got a simple voltage divider:
If you were to tack a load resistor onto the output of your circuit and use node voltage analysis to solve for the output voltage, then you should be able to rearrange the resulting expression into the form of the voltage divider expression and just pick out Vth and Rth by inspection, thus solving for both at the same time.
This technique can be very handy; as long as the circuit in question has at least one power source (so any controlled sources can be "stimulated"), you don't have to bother with sticking external sources onto the output to find resistances or voltages.
If you consider a general Thevenin model with a resistive load attached, you've really got a simple voltage divider:
If you were to tack a load resistor onto the output of your circuit and use node voltage analysis to solve for the output voltage, then you should be able to rearrange the resulting expression into the form of the voltage divider expression and just pick out Vth and Rth by inspection, thus solving for both at the same time.
This technique can be very handy; as long as the circuit in question has at least one power source (so any controlled sources can be "stimulated"), you don't have to bother with sticking external sources onto the output to find resistances or voltages.
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ainster31
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Sorry, I wasn't clear enough in my original question. I'm not sure how I forgot put these details but here they are now. I've calculated the Thevenin equivalent and I'm currently trying to get the Norton equivalent. I realize that I can just use source transformation to convert from the Thevenin equivalent to the Norton equivalent but I am trying to get the Norton equivalent directly from the circuit.
Since I already did the Thevenin equivalent, I already know that Vx=10/21 V and Rth=10/21 Ω. Now, I'm trying to calculate IN. I've connected nodes a and b but I am having trouble applying mesh analysis. I've already applied mesh analysis to mesh 1 but after looking at it, it seems to be incorrect. Here is the correct mesh analysis:
$$-50+12{ i }_{ 1 }+60({ i }_{ 1 }-{ i }_{ 2 })=0\\ -50+12{ i }_{ 1 }+\frac { 10 }{ 21 } =0$$
Edit: Actually, I don't even know what Vx is. That was incorrect.
I've tried applying nodal analysis at node X:
$$\frac { { v }_{ x }-50 }{ 12 } +\frac { { V }_{ x } }{ 60 } +2{ V }_{ x }+{ I }_{ N }=0$$
but I'm still stuck.
Since I already did the Thevenin equivalent, I already know that Vx=10/21 V and Rth=10/21 Ω. Now, I'm trying to calculate IN. I've connected nodes a and b but I am having trouble applying mesh analysis. I've already applied mesh analysis to mesh 1 but after looking at it, it seems to be incorrect. Here is the correct mesh analysis:
$$-50+12{ i }_{ 1 }+60({ i }_{ 1 }-{ i }_{ 2 })=0\\ -50+12{ i }_{ 1 }+\frac { 10 }{ 21 } =0$$
Edit: Actually, I don't even know what Vx is. That was incorrect.
I've tried applying nodal analysis at node X:
$$\frac { { v }_{ x }-50 }{ 12 } +\frac { { V }_{ x } }{ 60 } +2{ V }_{ x }+{ I }_{ N }=0$$
but I'm still stuck.
Last edited:
ainster31
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gneill said:
Hmmm, Vx would be 0V, right? And that means I can remove the 60 ohm resistor and the dependent current source, right?
ainster31
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Haha, I got it. Wow, I was stressing out over such a simple problem.