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 KVL with Generic Elements
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Kirchhoff's Laws
Using KVL to find voltages across generic elements
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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