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Okay, here's a problem that we[br]were working in class today, and

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I would like to just go over[br]this example again for you.

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We want to be able to find Vx.

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We can see we have a lot of resistors here[br]we can combine in series and parallel.

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Let's first color code all of our nodes.

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Here is a red node,[br]that's a extraordinary node.

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Here is an orange node,[br]that's another extraordinary node.

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Here is a blue node, also extraordinary.

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And we can see that at the bottom,[br]we have a black node that is also

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an extraordinary node that[br]includes all of these elements.

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Well let's begin by combining[br]our resistors in parallel.

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We can see that,[br]these two 16 are in parallel,

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because they are red on the top and[br]black on the bottom.

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When we have resistors in parallel,[br]we combine them in this way and

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if they happen to be[br]equal as the two 16 are.

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Then we end up with half[br]of the original resistance.

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So, when you combine these two in[br]parallel 16 and parallel with 16,

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it's going to give us 8.

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We can now see the 4 and[br]the 8 are in series,

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because they have a single[br]ordinary node between them.

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So, when we combine those in series[br]we just add them up, and the 8 and

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4 together, right here,[br]is going to give me a resistance of 12.

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Now, we have a 12 from yellow to black and[br]yellow to black,

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those two are in parallel.

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So 12 and 12 in parallel,[br]because of the same going to give me 6.

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Now, something cool happens here.

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I end up with a 6 on a resistance right[br]here, which I can bring to the other side

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of my current source and[br]that's because, they have the same node

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across the topic and rearrange anything[br]that's connected in the same nodes.

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So, my 6 is going to come over there and[br]then the 6 and 6 in parallel,

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is going to get me something that is 3.

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So my final circuit,[br]is going to look like a 10 amp current

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source in parallel with 3 ohms,[br]and then I have a 4 and

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let's combine these in series 8,[br]and I want to find this voltage.

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There's not a minus there.

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I want to find Vx.

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Now, I also can see that 8 and[br]4 go together in series.

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But, because I want to find Vx, I need to[br]leave the element that it's across and

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not combine it with other stuff or else[br]it will get all mixed up in my circuit.

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Now, here's the circuit that we have, and

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I'm going to show you two different[br]ways of being able to solve it.