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184_notes:kirchoffs_rules [2018/10/08 19:15] – [Step 2: Identify the Nodes and write out the Node Rule equations] tallpaul | 184_notes:kirchoffs_rules [2021/03/04 17:02] – [Step 1: Pick the direction of current in each branch of the circuit] bartonmo | ||
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===== Using Loop and Node Rules to Solve Circuits ===== | ===== Using Loop and Node Rules to Solve Circuits ===== | ||
- | So far this week, we have talked about how to deal with circuit elements that are in series and in parallel. We can use these rules for resistance, along with Ohm's law, to figure out the current and voltage at every point in the circuit. However, how do you solve circuits that are neither in series or parallel? Or when there are multiple voltage sources? For circuits that don't follow the series/ | + | So far this week, we have talked about how to deal with circuit elements that are in [[184_notes: |
==== Example and Steps for Node/Loop Rules ==== | ==== Example and Steps for Node/Loop Rules ==== | ||
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==== Step 1: Pick the direction of current in each branch of the circuit ==== | ==== Step 1: Pick the direction of current in each branch of the circuit ==== | ||
[{{ 184_notes: | [{{ 184_notes: | ||
- | The first thing we need to do when solving these problems is to pick a direction for the current in each branch of the circuit. This is very similar to picking a coordinate system, just in the context of circuits. In the circuit below, we have picked the directions for the currents labeled now as $I_1$, $I_2$, and $I_3$. You can pick which ever directions you want in this step. For example, we could have picked $I_3$ to point up instead of down (or similarly for the other currents). It doesn' | + | The first thing we need to do when solving these problems is to pick a direction for the current in each branch of the circuit. This is very similar to picking a coordinate system, just in the context of circuits. In the circuit below, we have picked the directions for the currents labeled now as $I_1$, $I_2$, and $I_3$. You can pick which ever directions you want in this step. For example, we could have picked $I_3$ to point up instead of down (or similarly for the other currents). |
==== Step 2: Identify the Nodes and write out the Node Rule equations ==== | ==== Step 2: Identify the Nodes and write out the Node Rule equations ==== | ||
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and for Point E, this equation would be: | and for Point E, this equation would be: | ||
- | $$\text{Node E: } I_3=I_1+I_2$$ | + | $$\text{Node E: } I_3+I_2=I_1$$ |
You'll notice that the Node equations for Points B and E are exactly the same (just flipped as to which currents are going " | You'll notice that the Node equations for Points B and E are exactly the same (just flipped as to which currents are going " | ||
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$$\text{Loop ABEDA: | $$\text{Loop ABEDA: | ||
- | $$\text{Loop BCFEB: | + | $$\text{Loop BCFEB: |
- | $$\text{Loop ABCFEDA: | + | $$\text{Loop ABCFEDA: |
Once you have the loop equations written out, you can always substitute $\Delta V = IR$ to make better use of your knowns/ | Once you have the loop equations written out, you can always substitute $\Delta V = IR$ to make better use of your knowns/ |