KVL with Generic Elements
Fall 2018
Kirchhoff's Laws
Using KVL to find voltages across generic elements
Learn It!
Pre-Requisite Knowledge
Goal
Using KVL
Use KVL to find the voltages across generic elements in a circuit
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Find the values of \(V_1\) and \(V_2\) in the diagram at left.

\( \begin{equation} a. V_1 = 1 \text{ V} \text{ and } V_2 = 13 \text{ V} \\b. V_1 = 1 \text{ V} \text{ and } V_2 = 11 \text{ V} \\c. V_1 = 5 \text{ V} \text{ and } V_2 = 7 \text{ V} \\d. V_1 = 7 \text{ V} \text{ and } V_2 = 5 \text{ V} \\e. V_1 = 7 \text{ V} \text{ and } V_2 = 19 \text{ V} \end{equation} \)
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What are these boxes?
Part 1
Find the first unknown voltage
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Let's pick a loop to analyze. We would prefer to use a loop that contains only one unknown. The left loop has both \(V_1\) and \(V_2\), but the top one contains only \(V_1\).
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Finding the signs
\[+V_1 -4 +3 = 0\]
Final KVL Equation
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Reasoning behind this loop
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Alternative loop
\[V_1 = 1 \]
Combining terms and moving the constants to the right hand side gives us an answer.
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What if we got a negative value?
Part 2
Finding the second unknown voltage
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Now that we have \(V_1\), we can find another loop that gives us \(V_2\).
\[+V_2 + V_1 - 12 = 0\]
Now we use KVL again. The voltage across the 12 V element is a drop, so it appears as negative in our equation.
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Why this loop?
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Solve KVL equation
\[V_2 = 11\]
Substitute \(V_1=1\)
\[V_1 = 1 \text{ V} \text{ and } V_2 = 11 \text{ V}\]
Choice \(b\) was the correct answer