KCL with Generic Elements
Fall 2018
Kirchhoff's Laws
Using KCL to find currents through generic elements
Learn It!
Pre-Requisite Knowledge
Goal
Using KCL
Use KCL to find the currents through generic elements in a circuit
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Find the values of \(I_1\) and \(I_2\) in the diagram at left.

\( \begin{equation} a. I_1 = 0.3\text{ A}\text{ and } I_2 = 0.6\text{ A} \\b. I_1 = 0.3\text{ A}\text{ and } I_2 = 0.4\text{ A} \\c. I_1 = 0.4\text{ A}\text{ and } I_2 = 0.4\text{ A} \\d. I_1 = 0.4\text{ A}\text{ and } I_2 = 0.5\text{ A} \\e. I_1 = 0.5\text{ A}\text{ and } I_2 = 0.6\text{ A} \end{equation} \)
Part 1
Find one unknown current
\(\Sigma I_{in}\; =\; \Sigma I_{out}\)
KCL is "Kirchhoff's Current Law." It states that the current flowing into a node must be equal to the current that flows out of the node.
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Limits of KCL
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Find KCL equation for one node
\[I_2 + 0.1 = 0.5\]
KCL expression for node at the bottom of the circuit.
\[I_2 = 0.4\]
Answer for Part 1
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What about the unlabeled element?
Part 2
Find the second unknown current
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Find KCL for second node
\[I_1 = 0.4 - 0.1 = 0.3 \]
Substitute \(I_2 = 0.4 \)
\[I_1 = 0.3 \text{ A} \text{ and } I_2 = 0.4\text{ A}\]
Choice B was the correct answer
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Alternate Node