6.1 Voltage, Current, Resistance, and Ohm’s Law

Why basic electricity leads the DOS topic list

The New York Department of State (DOS) Security or Fire Alarm Installer written exam lists basic electricity first among the bulletin topic areas. That order matches the qualifying course. Module 1 of the 81-hour program (19 NYCRR 196.8) is 15 hours of installations, standards, codes, and techniques, and Module 1.III Basic Electricity is 10 of those 15 hours — the densest electricity block in the curriculum. Independent OpenExamPrep material in this chapter trains the same three quantities you will use on every initiating device circuit (IDC), notification appliance circuit (NAC), auxiliary power output, and, in Chapter 9, battery calculation: voltage, current, and resistance, joined by Ohm’s law.

The written sitting is closed-book. You will not receive a formula sheet. You must rearrange V = I × R in your head, convert milliamperes and kilohms without dropping a factor of 1,000, and recognize those numbers on a 24 VDC fire alarm control unit (FACU) or a 12 VDC security panel. This license covers security or fire alarm installing, so both voltages belong in your practice set.

Voltage, current, and resistance

A complete circuit needs a source, a closed path, and a load. If the path is open, current is zero. If the load is replaced by a near-zero resistance (a short), current is limited only by the rest of the circuit and the panel’s protection.

Voltage (symbol V or E) is electrical pressure, also called electromotive force (EMF) when you mean the source. The unit is the volt (V). Typical fire alarm NACs and many IDCs are 24 VDC. Many security control panels, motion detectors, and auxiliary outputs are 12 VDC. Voltage is measured across two points (in parallel with the element you are measuring).

Current (symbol I) is the flow of electric charge. The unit is the ampere (A). One ampere equals one coulomb per second. Alarm work lives in milliamperes: 1 A = 1,000 mA. A listed horn-strobe might nameplate 75 mA at 24 V. Two-wire smoke detectors draw only tens to a few hundred microamperes (µA) in standby. Supervision current through an end-of-line (EOL) resistor is usually a few milliamperes. Current is measured in the path (Chapter 7.3 covers meter connections).

Resistance (symbol R) opposes current. The unit is the ohm (Ω). 1 kΩ = 1,000 Ω; 1 MΩ = 1,000,000 Ω. A typical listed EOL on conventional fire panels is 4.7 kΩ (4,700 Ω); 2.2 kΩ is also widely used. Some panels specify 3.9 kΩ, 10 kΩ, or another value. Use the listed value printed on the panel door or in the installation instructions. Do not carry one manufacturer’s resistor onto another panel.

A water-pipe analogy is fair for these three words: voltage is pressure, current is flow, resistance is a restriction. Raise pressure or lower restriction and flow increases. The analogy does not explain polarity or semiconductors, but it is enough to remember the direction of Ohm’s law.

Ohm’s law — three forms, one relationship

V = I × R

I = V / R

R = V / I

Keep the units consistent: volts, amperes, ohms. Convert before you divide:

• 75 mA = 0.075 A
• 4.7 kΩ = 4,700 Ω
• 5.11 mA = 0.00511 A

A reliable arithmetic trap is 24 / 4.7 = 5.1 amperes. That 4.7 is kilohms, so the current is 5.1 milliamperes — one thousand times smaller.

Worked example A — I = V / R (EOL supervision current)

A conventional IDC presents 24 V across a 4.7 kΩ listed EOL at the last device. Ignore wire resistance on this first pass.

1. Convert: 4.7 kΩ = 4,700 Ω.
2. I = V / R = 24 / 4,700 = 0.005106 A.
3. Convert: 0.005106 × 1,000 = 5.11 mA (about 5.1 mA).

If that panel’s door specified a 2.2 kΩ EOL instead:

I = 24 / 2,200 = 0.01091 A = 10.9 mA.

Those few milliamperes are supervision current. The zone circuit watches them. If the pair opens, current falls toward zero and the panel indicates trouble. If a normally-open initiating device closes, loop resistance collapses and current rises — alarm on a conventional IDC. Full meter diagnosis of opens, shorts, and ground faults is Chapter 7.3; the qualitative picture starts here.

Worked example B — R = V / I (appliance equivalent resistance)

A listed 24 V horn-strobe nameplate shows 75 mA at 24 VDC. Treat 75 mA as a worked-example nameplate, not as a claim that every candela rating draws 75 mA.

1. 75 mA = 0.075 A.
2. R = V / I = 24 / 0.075 = 320 Ω.

320 Ω is the equivalent load of that appliance at 24 V. You do not install a 320 Ω resistor. You use 320 Ω when you combine loads in Section 6.2.

If the nameplate were 125 mA at 24 V: R = 24 / 0.125 = 192 Ω.

Worked example C — V = I × R (copper voltage drop on a NAC)

Uncoated copper 18 AWG is about 6.39 Ω per 1,000 ft at ordinary room temperature (about 20 °C). That is the standard copper-wire figure trade courses use for drop problems, and it is the value this guide uses. NEC Chapter 9, Table 8 is a different column: it publishes direct-current resistance at 75 °C, where solid uncoated 18 AWG reads about 7.77 Ω per 1,000 ft, so a Table 8 calculation produces a larger, more conservative drop. Use whichever figure the problem or the design hands you, and say which one you used. A NAC run is 200 ft one-way, so the pair’s round-trip length is 400 ft.

1. R_wire = 6.39 Ω/1,000 ft × (400 / 1,000) = 2.556 Ω.
2. Six 75 mA appliances in parallel draw I_T = 6 × 0.075 = 0.450 A (see Section 6.2).
3. V_drop = I × R = 0.450 × 2.556 = 1.15 V.
4. Voltage at the last device ≈ 24.00 − 1.15 = 22.85 V.

Many listed 24 V notification appliances publish an operating window near 16–33 VDC on the nameplate. 22.85 V still sits inside that typical window. Lengthen the run, add appliances, or stay on 18 AWG and you eat the margin. That is why installers upsize to 16 AWG or 14 AWG on long NACs.

Worked example D — same law on 12 V security power

A 12 VDC motion detector nameplate shows 25 mA.

R = 12 / 0.025 = 480 Ω.

Check: I = 12 / 480 = 0.025 A = 25 mA. Same three letters, different system voltage. Do not assume every loop on this exam is 24 V.

Polarity, conventional current, and reading a meter

Conventional current is drawn from the positive terminal through the load to the negative terminal. That is how prints, terminal strips, and polarized device markings are labeled: + to +, − to −. Electron flow is the opposite direction — electrons leave the negative terminal and move toward the positive. You do not need electron-flow arithmetic on the DOS exam; you need the distinction so a textbook talking about electrons does not reverse your meter leads.

A digital multimeter (DMM) on DC volts: red lead on the more positive point, black lead on COM (more negative). A negative display usually means the leads are reversed relative to actual polarity. The magnitude is still the voltage. Chapter 7.3 is the meters chapter; this is enough to land a polarized horn-strobe and to trust a minus sign.

Open versus short (qualitative preview):

• Open (broken conductor, loose pigtail, EOL never landed): resistance theoretically infinite, current ≈ 0. You may measure source voltage across the break.
• Short (conductors touching, a contact closed, a staple through the jacket): resistance ≈ 0. Voltage across the short ≈ 0. Current is large and is limited by remaining resistance and the panel’s protection.

Polarized horns, strobes, and two-wire smokes include a series diode or polarized electronics. Reverse the pair and the device will not operate as intended even though a meter still shows about 24 V. Classic NAC supervision used reverse polarity in standby so polarized appliances stayed silent while current still flowed through the EOL; alarm drove the pair to forward polarity. Confirm the listed method in the panel manual — newer NACs may supervise differently — but polarity marks exist for this reason.

Prefixes, copper, and exam traps

Copper resistance rises with length and with temperature, and falls as the conductor gets thicker (smaller AWG number). Cable jackets (FPL/FPLR/FPLP from Chapter 5) are insulation, not a second conductor you can ignore. The FACU common (DC negative) is a circuit reference; it is not a substitute for equipment grounding or for the building grounding electrode system. Line-voltage conductors to the panel remain electrician work under 19 NYCRR 195.2; this chapter’s arithmetic is the low-voltage side of that boundary.

Exam traps

• Forgetting to convert mA or kΩ and landing off by 1,000.
• Using one-way footage for voltage drop instead of round-trip pair length.
• Treating nameplate milliamperes as amperes (75 A instead of 75 mA).
• Inventing an EOL value instead of using the listed value on the panel door.
• Reading a negative DMM value as no voltage instead of reversed leads.

Memorize the three rearrangements until they are automatic. Section 6.2 places several resistances in the same circuit. Section 6.3 turns V and I into watts and watt-hours.