184_notes:examples:week6_node_rule

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Suppose you have the circuit below. Nodes are labeled for simplicity of discussion. 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 Current Node Rule. Draw the direction of the current as well.

Circuit with Nodes

Facts

  • $I_1=8 \text{ A}$, $I_2=3 \text{ A}$, and $I_3=4 \text{ A}$.
  • $I_1$, $I_2$, and $I_3$ are directed as pictured.

Lacking

  • All other currents (including their directions).

Approximations & Assumptions

  • The current is not changing.
  • All current in the circuit arises from other currents in the circuit.

Representations

  • We represent the situation with diagram given.
  • We represent the Node Rule as $I_{in}=I_{out}$.

Let's start with node $A$. Incoming current is $I_1$, and outgoing current is $I_2$. How do we decide if $I_{A\rightarrow B}$ is incoming or outgoing? We need to bring it back to the Node Rule: $I_{in}=I_{out}$. Since $I_1=8 \text{ A}$ and $I_2=3 \text{ A}$, we need $I_{A\rightarrow B}$ to be outgoing to balance. To satisfy the Node Rule, we set $$I_{A\rightarrow B} = I_{out}-I_2 = I_{in}-I_2 = I_1-I_2 = 5 \text{ A}$$

  • 184_notes/examples/week6_node_rule.1506520728.txt.gz
  • Last modified: 2017/09/27 13:58
  • by tallpaul