To calculate voltage drop in a series circuit, you multiply the circuit's total current by the resistance of the specific segment you are analyzing ($V_{drop} = I_{total} \times R_{segment}$). In a 24V DC home security or fire alarm supervisory loop, the components share the same current path. If you miscalculate the drop across long wire runs, the final relay coil starves, causing nuisance alarms or failure to trip. By the end of this guide, you will have a complete mathematical model for a 24V series loop, a clear understanding of why series topology is mandatory for safety, and a concrete wire-sizing decision.
The Series Topology: Node Map and Core Behavior
Before running wire through your walls, you need a map. In a standard 24V DC Normally Closed (NC) security loop, the components are daisy-chained. Here is the exact node topology we will analyze:
- Node A: Power Supply Positive (24V DC out)
- Node B: End of the outbound 22 AWG wire run (at the first sensor)
- Node C: Output of Sensor 1 (Honeywell 958 reed switch)
- Node D: Output of Sensor 2
- Node E: Output of Sensor 3
- Node F: Input of the main panel relay coil (Positive terminal)
- Node G: Output of the main panel relay coil (Negative terminal)
- Node H: Power Supply Negative (Return path via 22 AWG wire)
In home security and fire alarm wiring (guided by NFPA 72 standards), supervisory loops are wired in series using NC switches. If an intruder cuts the wire, the circuit opens, current drops to zero, the relay drops out, and the alarm triggers. If you wired these sensors in parallel, cutting a wire would only disable a single sensor while the rest of the loop remained closed, silently compromising your security. Series topology guarantees that any break in the chain is detected.
Design Walkthrough: How to Calculate Voltage Drop in Series Circuit
Let's move from theory to the workbench. We are designing a loop for a detached garage with three entry points. Here are the real-world component values we will use:
- Power Supply: Altronix SMP3 (Set to 24V DC output)
- Wire: 500 feet total of 22 AWG stranded copper security cable (250 ft outbound, 250 ft return). According to standard AWG resistance tables, 22 AWG copper is 16.14 $\Omega$ per 1,000 ft.
- Sensors: 3x Honeywell 958 NC magnetic reed switches. Closed contact resistance is approximately 0.5 $\Omega$ each.
- Load: 1x Omron G2R-1-DC24 general-purpose relay. Coil resistance is 1,150 $\Omega$.
Step 1: Calculate Total Resistance ($R_{total}$)
In a series circuit, resistances simply add up.
- Wire Resistance: $16.14 \times (500 / 1000) = 8.07 \Omega$
- Switch Resistance: $0.5 \Omega \times 3 = 1.5 \Omega$
- Relay Coil Resistance: $1,150 \Omega$
- $R_{total}$: $8.07 + 1.5 + 1150 = 1,159.57 \Omega$
Step 2: Calculate Total Current ($I_{total}$)
Using Ohm's Law ($I = V / R$):
$I = 24V / 1,159.57 \Omega = 0.02069 A$ (or 20.7 mA). Because it's a series circuit, this exact current flows through every node from A to H.
Step 3: Calculate the Voltage Drop per Segment
Now we answer the core question: how to calculate voltage drop in series circuit segments individually.
- Drop across the wire (Nodes A-B and G-H): $0.02069 A \times 8.07 \Omega = \mathbf{0.167 V}$
- Drop across the switches (Nodes B-E): $0.02069 A \times 1.5 \Omega = \mathbf{0.031 V}$
- Voltage remaining at the relay (Node F to G): $24V - 0.167V - 0.031V = \mathbf{23.802 V}$
The Omron relay requires at least 80% of its nominal voltage (19.2V) to pull in reliably. At 23.8V, our design has plenty of headroom. The wire drop of 0.167V is negligible here, but if we had used 26 AWG wire or extended the run to 2,000 feet, that drop would scale up and potentially starve the coil.
Behavior Table: What Breaks at the Extremes?
A series circuit is highly sensitive to single-point failures. Here is a comparison matrix showing exactly what happens to the voltage and current when one element shifts to an extreme state.
| Condition | Circuit State | Current Flow | Voltage at Relay (Node F-G) | System Result |
|---|---|---|---|---|
| Normal Operation | All switches closed, wire intact | 20.7 mA | 23.8 V | Relay pulled in; system secure. |
| Open Circuit | Wire cut or door opened (Switch opens) | 0 mA | 0 V (Full 24V appears across the open gap) | Relay drops out; ALARM TRIGGERS (Fail-safe). |
| Short Circuit | Wire insulation fails, bypassing a switch | 20.75 mA (slightly higher) | 23.9 V | Relay stays pulled in; SENSOR BYPASSED (Security compromised). |
| Relay Coil Short | Internal coil winding shorts out | Spikes to ~2.5 A | ~0 V | Power supply trips its internal overcurrent protection; system goes offline. |
Notice the short circuit row. This is why high-security installations use End-of-Line (EOL) resistors in parallel with the last switch, combined with series wiring, to detect both opens and shorts. But for basic series loops, an open is your primary failure mode to design for.
Breadboard and Field Testing: Step-by-Step Verification
Never bury 500 feet of wire in conduit without bench-testing the logic first. Grab your Fluke 117 (or equivalent True-RMS multimeter) and follow this verification sequence.
- De-energize and Isolate: Ensure the Altronix power supply is unplugged. Disconnect the relay coil from the circuit to test the field wiring independently.
- Continuity Check (The Loop): Set your meter to the continuity/diode setting. Place the red probe on Node A (wire out) and the black probe on Node H (wire return). With all three Honeywell switches closed, you should read a dead short (typically under 10 $\Omega$ accounting for your test leads and the 8.07 $\Omega$ wire). If it reads OL (Open Loop), you have a break in the run.
- Verify Switch Isolation: Open Switch 1. The meter should immediately read OL. Close it, open Switch 2, verify OL. This proves the switches are actually interrupting the series path and aren't accidentally wired in parallel.
- Energize and Measure Drops: Reconnect the Omron relay coil and plug in the 24V supply. Set your meter to DC Volts.
- Measure Node A to H: Confirm your source is actually outputting 24.0V DC. (Cheap supplies often float to 24.5V under no-load and sag to 23.5V under load).
- Measure Node A to B: Read the voltage drop across the outbound wire. It should read ~0.08V.
- Measure Node F to G: Read the voltage directly across the relay coil pins. It must read >19.2V. If it reads 23.8V as calculated, your design is validated.
Decision Path: Sizing Wire and Power for Your Run
When designing your own series loop, use this decision tree to lock in your wire gauge and power supply. Do not guess; let the run length dictate the copper.
| If your total wire run (out + back) is... | And your load current is... | Then select this AWG wire... | Expected Voltage Drop |
|---|---|---|---|
| Under 500 feet | < 50 mA (Standard relays) | 22 AWG | < 0.2 V (Negligible) |
| 500 to 1,500 feet | < 50 mA (Standard relays) | 18 AWG | < 0.5 V (Safe margin) |
| Over 1,500 feet | < 50 mA (Standard relays) | 16 AWG | < 0.6 V (Required for distance) |
| Any length | > 1.0 A (Sirens/Strobes) | 14 AWG or 12 AWG | Calculate via $V=IR$; keep drop < 1.5V |
For 90% of residential 24V DC security and HVAC interlock loops running under 1,000 feet total, buy a 1,000 ft spool of 18 AWG 2-conductor stranded copper cable (like Carol Brand or Belden). 18 AWG is the sweet spot: it is cheap, fits easily into standard screw terminals on Omron relays and Honeywell sensors without needing ferrules, and its 6.38 $\Omega$/1000ft resistance keeps your voltage drop well under 0.5V for low-current supervisory loops. Pair it with a regulated 24V 1.5A power supply to ensure the voltage doesn't sag when the relay coil initially pulls in.
Calculating voltage drop in a series circuit isn't just an academic exercise; it is the difference between a security system that catches an intruder and one that fails silently because the relay coil didn't get enough voltage to hold the contacts closed. Map your nodes, do the math with real component resistances, and always verify with a meter before closing up the panel.
