Spring 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
Find the values of $V_1$ and $V_2$ in the diagram at left.

$$$a. V_1 = 1 \text{ V} \text{ and } V_2 = 13 \text{ V} \\b. V_1 = 1 \text{ V} \text{ and } V_2 = 11 \text{ V} \\c. V_1 = 5 \text{ V} \text{ and } V_2 = 7 \text{ V} \\d. V_1 = 7 \text{ V} \text{ and } V_2 = 5 \text{ V} \\e. V_1 = 7 \text{ V} \text{ and } V_2 = 19 \text{ V}$$$
+
?
What are these boxes?
Part 1
Find the first unknown voltage
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 $V_1$.
+
⇨
Finding the signs
$+V_1 -4 +3 = 0$
Final KVL Equation
+
?
Reasoning behind this loop
+
!
Alternative loop
$V_1 = 1$
Combining terms and moving the constants to the right hand side gives us an answer.
+
?
What if we got a negative value?
Part 2
Finding the second unknown voltage
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.
+
?
Why this loop?
+
⇨
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