184_notes:examples:week6_node_rule

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184_notes:examples:week6_node_rule [2018/02/03 22:33] – [Solution] tallpaul184_notes:examples:week6_node_rule [2018/06/11 19:55] – curdemma
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 +[[184_notes:current|Return to current in wires]]
 +
 =====Example: Application of Node Rule===== =====Example: Application of Node Rule=====
 Suppose you have the circuit below. You are given a few values: $I_1=8 \text{ A}$, $I_2=3 \text{ A}$, and $I_3=4 \text{ A}$. Determine all other currents in the circuit, using the [[184_notes:current#Current_in_Different_Parts_of_the_Wire|Current Node Rule]]. Draw the direction of the current as well. Suppose you have the circuit below. You are given a few values: $I_1=8 \text{ A}$, $I_2=3 \text{ A}$, and $I_3=4 \text{ A}$. Determine all other currents in the circuit, using the [[184_notes:current#Current_in_Different_Parts_of_the_Wire|Current Node Rule]]. Draw the direction of the current as well.
-{{ 184_notes:6_nodeless.png?300 |Circuit}}+[{{ 184_notes:6_nodeless.png?300 |Circuit}}]
  
 ===Facts=== ===Facts===
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 ===Representations=== ===Representations===
 For simplicity of discussion, we label the nodes in an updated representation: For simplicity of discussion, we label the nodes in an updated representation:
-{{ 184_notes:6_nodes.png?300 |Circuit with Nodes}}+[{{ 184_notes:6_nodes.png?300 |Circuit with Nodes}}]
  
 ====Solution==== ====Solution====
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 $$I_{D\rightarrow battery} = I_{out} = I_{in} = I_{B\rightarrow D}+I_{B\rightarrow D} = 8 \text{ A}$$ $$I_{D\rightarrow battery} = I_{out} = I_{in} = I_{B\rightarrow D}+I_{B\rightarrow D} = 8 \text{ A}$$
  
-Notice that $I_{D\rightarrow battery}=I_1$. This will always be the case for currents going in and out of the battery (approximating a few things that are usually safe to approximate, such as a steady current). In fact, we could have treated the battery as another node in this example. Notice also that if you incorrectly reason about the direction of a current (incoming or outgoing), the calculation will give a negative number for the current. The Node Rule is self-correcting. A final diagram with directions is shown below.+Notice that $I_{D\rightarrow battery}=I_1$. This will always be the case for currents going in and out of the battery (approximating a few things that are usually safe to approximate, such as a steady current). In fact, we could have treated the battery as another node in this example. Notice also that if you incorrectly reason about the direction of a current (incoming or outgoing), the calculation will give a negative number for the current. The Node Rule is self-correcting. A final representation with directions is shown below.
  
-{{ 184_notes:6_nodes_with_arrows.png?300 |Circuit with Nodes}}+[{{ 184_notes:6_nodes_with_arrows.png?300 |Circuit with Nodes}}]
  • 184_notes/examples/week6_node_rule.txt
  • Last modified: 2021/06/08 00:51
  • by schram45