Electrician How-To Lesson · Apprentices and classroom instructors
Imagine two learners looking at the same circuit drawing. One sees two resistors beside each other and calls them parallel. The other traces the connections and realizes that current has only one complete path through both.
The difference is not who remembers a formula faster. It is who reads the connections before choosing the formula.
This hypothetical classroom example explains the purpose of this lesson: reason about the circuit arrangement, then calculate. We will use ideal DC sources, ideal connecting wires and ideal resistors on paper. This is not a procedure for installing, modifying or testing energized equipment, and the calculations are not instructions for equipment or conductor sizing.
You will learn to identify a single series path, recognize branches connected across the same two nodes and predict what happens when a path opens in a simple circuit model.
Your finished exercise will include a path description, an expected behavior and a calculation that supports your explanation. Our original EDU Circuit Reasoning Worksheet asks learners to explain behavior before calculating. That is the habit we are practicing here.
A schematic represents electrical relationships. Components drawn close together are not necessarily connected in the way their position suggests. Trace the indicated connections and identify junctions using the drawing's own conventions.
A node is a connected point or set of points treated as having the same potential in this ideal-wire model. For a straightforward parallel arrangement, each branch connects to the same two nodes. For a straightforward series arrangement, the components lie along one path without an intervening branch that divides current.
If a connection is unclear, do not guess from spacing or line crossings. Resolve the notation before deciding which circuit rule to use. This is why symbol and legend reading belongs alongside calculation practice.
In the simple series model, the same current passes through each resistor. The total resistance is the sum of the individual resistances. The voltage drops across the resistors add to the source voltage around the loop.
Use a new classroom example: an ideal 24 V DC source supplies a 4-ohm resistor and an 8-ohm resistor in series.
First explain the path: current has one complete route through both resistors. Next calculate the total resistance: 4 + 8 = 12 ohms. The current is 24 V ÷ 12 ohms = 2 A.
Now calculate each voltage drop. Across the 4-ohm resistor, V = 2 A × 4 ohms = 8 V. Across the 8-ohm resistor, V = 2 A × 8 ohms = 16 V. The drops add to 24 V.
The voltage drops are not equal because the resistances are not equal. The current is equal because these resistors are on the same single path. Those are different statements, and the distinction matters.
Now place a 6-ohm resistor and a 12-ohm resistor in separate branches across an ideal 12 V DC source.
Each resistor is connected across the same two nodes, so each has 12 V across it. The 6-ohm branch carries 12 ÷ 6 = 2 A. The 12-ohm branch carries 12 ÷ 12 = 1 A. The source supplies the sum, 3 A, in this model.
The equivalent resistance is therefore 12 V ÷ 3 A = 4 ohms. It is lower than either branch resistance. That is a useful reasonableness check for ideal positive resistances in parallel.
Do not say that parallel branches always carry the same current. They share the same voltage across the common nodes; their currents depend on their resistance. Equal resistances would produce equal branch currents in this ideal example, but unequal resistances do not.
OpenStax’s resistor-circuit explanation develops these series and parallel relationships. Use it as a reference when you want to review the reasoning behind the equations.
Return to the simple series example. If the only path is opened, the ideal steady-state current stops throughout that path. There is no complete loop for current through the series resistors.
In the simple parallel example, suppose only the 6-ohm branch opens while the ideal source and the other branch remain connected. Current in the opened branch is zero. The 12-ohm branch still has 12 V across it and carries 1 A. Source current becomes 1 A.
Those conclusions depend on the stated model. An actual system may contain shared connections, controls, protection or additional components. Do not turn a classroom branch example into a promise about how real equipment will behave.
On paper, draw two clearly labeled ideal DC circuits. Use your instructor's approved symbols and identify the source and resistor values.
Circuit A: a 15 V source with 3-ohm and 2-ohm resistors in series. Circuit B: a 12 V source with 4-ohm and 12-ohm resistors in parallel.
For each circuit:
For Circuit A, the total resistance is 5 ohms and current is 3 A. The drops are 9 V and 6 V. For Circuit B, branch currents are 3 A and 1 A, so source current is 4 A. These results check this article's new examples, not the original worksheet's answers.
This lesson draws on the original EDU Circuit Reasoning Worksheet, page 29 of our training packet, which asks learners to explain series and parallel behavior and open paths.
Complete the conceptual questions above using a clearly stated classroom model. This lesson does not authorize taking measurements; any hands-on activity belongs within the instructor's approved training and safety procedures.
Bring your drawing and explanation to your next learning session. If a partner reaches a different answer, compare the connections and assumptions first. Working through that difference builds understanding you can explain to someone else.
I’m Wilson Matthew Betances, and my mission is simple: Building the People Who Build Things. Take one thing from this lesson and put it to work. If it helped, keep learning with us.