Series DC Circuits and Kirchhoff's Voltage Law

What Is a Series Circuit?

A series circuit has only one current path. Every component — resistors, lamps, or any other load — is connected end-to-end so the same current flows through each one. If you break the path anywhere, current stops everywhere. That single-path behavior is the key fact behind every calculation and every troubleshooting step in this lesson.

Kirchhoff's Voltage Law (KVL)

Gustav Kirchhoff stated the law in the mid-1800s, and it has been confirmed by countless measurements ever since: the algebraic sum of all voltages around any closed loop equals zero. In practical terms, this means the source voltage equals the sum of all the voltage drops across the resistors in the loop.

> KVL statement: V_source = V₁ + V₂ + V₃ + … + Vₙ

Each resistor in a series circuit drops a portion of the total supply voltage. A resistor with a larger resistance drops a larger share; a resistor with a smaller resistance drops a smaller share. The drops must add up exactly to the supply — no more, no less. This is not an approximation; it is a fundamental law of circuit behavior.

Calculating Voltage Drops in a Series Circuit

Follow these steps for any series circuit:

1. Find total resistance. Add all resistor values: R_total = R₁ + R₂ + R₃ + … + Rₙ

2. Find series current. Apply Ohm's Law: I = V_source ÷ R_total. This one current flows through every component.

3. Find each voltage drop. Apply Ohm's Law to each resistor: Vₙ = I × Rₙ

4. Verify with KVL. Sum all drops and confirm the total equals V_source.

Step 4 is your built-in check. If the sum does not equal the source voltage within rounding error, recheck your arithmetic before you touch the breadboard.

Using a DMM to Measure Voltage

A digital multimeter (DMM) measures voltage in parallel with the component — place the probes across the resistor, not in series with it. Set the DMM to DC Volts and select a range equal to or higher than the expected reading. Touch the red probe to the more-positive side and the black probe to the more-negative side for a positive reading.

For this lab, your measurements must fall within ±5% of the calculated value to confirm the prediction. Differences larger than that usually mean a wiring error, a wrong resistor, or a faulty connection.

KVL and Troubleshooting: The Open Circuit

KVL is your most powerful troubleshooting tool in a series circuit. When one element is open (broken wire, failed component, missing jumper), the full source voltage appears across the open, and zero volts appears across every good resistor. Here is why: with no current flowing, Ohm's Law says V = I × R = 0 × R = 0 V across each resistor. The source voltage is undiminished and must appear somewhere in the loop — it appears entirely across the open gap.

To locate an open in a series string:

• Measure voltage across each element in turn.
• The element showing full source voltage is the open (or is connected directly across the open).
• Good resistors will read 0 V when an open is elsewhere in the loop.

This systematic voltage-measurement method is faster and safer than probing with a continuity tester on a live circuit.

Safety in This Lab

Electrical safety — The DC power supplies used in this lab operate at low voltages (typically 12 V or less) and are not a serious electrocution hazard at that level. However, safe work habits must be established now because they carry over to higher-voltage work later in the program.

• Build the circuit with the power supply OFF. Turn on power only when the circuit is complete and you are ready to measure.
• Do not exceed the power rating of resistors. Calculate the power dissipated (P = I² × R or P = V² ÷ R) and confirm it is well below the component's rated wattage. Overloaded resistors can burn.
• Inspect DMM test leads before each use. Cracked insulation or exposed bare wire at the probe tips is a shock hazard on higher-voltage equipment. Replace damaged leads immediately.
• Keep the work area dry. Liquids and electronics do not mix.
• Report any component that becomes warm to the touch to the instructor before continuing.

There is no lockout/tagout requirement for bench-level DC supplies, but students must understand that the habit of de-energizing before rewiring protects both the worker and the equipment in every voltage class.

Connecting This Lesson to Your Credentials

KVL is tested directly on the ETA CET written examination. The BICSI Installer credential focuses on cabling systems, but an installer who understands how voltage distributes in a series DC path can diagnose powered cabling faults confidently. Mastering these fundamentals now builds the foundation for AC circuits, signal transmission, and the fiber-optic power-budget calculations you will encounter later in the program.