Understanding series circuits

What you should be able to do

Identify a single series path, calculate its total resistance and current, then check the voltage drops across two resistors.

Core Idea

Components are in series when the same current passes through them in sequence without a branching path between them. For ideal series resistors, total resistance is the sum of their resistances. Each voltage drop equals that shared current times the individual resistance. In this one-source loop, the drops sum to the source voltage.

Worked through

The fictional worksheet gives: Source: 24 V DC. R1: 100 Ω. R2: 200 Ω. Assumptions: ideal source, constant resistances and negligible wire resistance.

Step 1 — Add the resistances. R total = 100 Ω + 200 Ω = 300 Ω.

Step 2 — Calculate current using the complete loop resistance. I = 24 V ÷ 300 Ω = 0.08 A = 80 mA. The current is 80 mA through R1 and also 80 mA through R2. It does not become smaller after the first resistor.

Step 3 — Calculate the individual voltage drops. V1 = 0.08 A × 100 Ω = 8 V. V2 = 0.08 A × 200 Ω = 16 V.

Step 4 — Check the sum. 8 V + 16 V = 24 V, matching the source. The larger resistor has the larger voltage drop because the current is the same through both.

Drawing Exercise

On a copy of this worksheet, rotate the page and trace the loop again. Nothing about the electrical relationship changes. Now imagine moving R2's drawn position to the bottom return line while retaining the same connections. It is still in the same series path. Physical appearance alone does not define a circuit.

Original Practice

A second worksheet specifies 12 V, R1 = 100 Ω and R2 = 300 Ω in series. Find total resistance, loop current and the two drops.

Answer:

R total = 400 Ω. I = 12 ÷ 400 = 0.03 A = 30 mA. V1 = 0.03 × 100 = 3 V. V2 = 0.03 × 300 = 9 V. Check: 3 V + 9 V = 12 V.

WHAT IF THE LOOP OPENS? A disconnected series connection interrupts this simple loop. With no other sources or paths in the model, steady current is zero through both resistors. The source can still maintain voltage across the open gap. “No current” is not the same statement as “no voltage.”

Scope And Application

This is a resistor-network lesson, not permission to connect readers, cameras or other rated devices in series. Their internal electronics and required terminal voltages may make that inappropriate. An actual supervised security or fire-alarm circuit may contain contacts, end-of-line components and electronic monitoring. Its topology and permitted wiring come from the equipment documentation; the familiar word “loop” alone does not prove that the entire circuit matches this resistor model. The drawing also omits protection and switching for clarity. It is not a field installation drawing.

Self-Check

Where beginners go wrong

Voice Recap

Series means one path. Add the resistances, calculate the shared current, then calculate each voltage drop. In our example, 24 volts drives 80 milliamps through 100 ohms and 200 ohms. The drops are eight volts and sixteen volts, adding to twenty-four.

Sources