184_notes:examples:week6_node_rule [Projects & Practices in Physics]

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--- 184_notes:examples:week6_node_rule [2018/02/03 22:33] – [Solution] tallpaul
+++ 184_notes:examples:week6_node_rule [2021/06/08 00:51] (current) – schram45
@@ Line 1: / Line 1: @@
+[[184_notes:current|Return to current in wires]]
 =====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.
-{{ 184_notes:6_nodeless.png?300 |Circuit}}
+[{{ 184_notes:6_nodeless.png?300 |Circuit}}]
 ===Facts===
@@ Line 13: / Line 15: @@
 ===Representations===
 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}}]
+<WRAP TIP>
+===Assumption===
+We will assume we have a perfect battery to supply a steady current to the circuit and will not die over time.
+</WRAP>
 ====Solution====
@@ Line 40: / Line 47: @@
  $I_{D\rightarrow battery} = I_{out} = I_{in} = I_{B\rightarrow D}+I_{B\rightarrow D} = 8 \text{ A}$
-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}}]