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BLD-HVAC07-03 · Lesson 2 · 13.5 clock hours · theory

Electrical Theory: Voltage, Current, Resistance, and Power

Objective. Students will apply Ohm's Law and the power formula to calculate unknown values in HVAC/R circuit problems and predict meter readings within ±5% of actual measured values.

Why Electrical Theory Matters in HVAC/R

Every HVAC/R system depends on electricity to run compressors, fans, pumps, and control circuits. A technician who understands voltage, current, resistance, and power can read a nameplate, size a transformer, trace a fault, and predict what a meter will show — before touching a single wire. This lesson builds that foundation.

Voltage, Current, and Resistance

Voltage (V) is electrical pressure — the force that pushes electrons through a circuit. It is measured in volts (V) with a voltmeter connected in parallel across the component.

Current (I) is the flow of electrons past a point in the circuit. It is measured in amperes (A) with an ammeter connected in series, or with a clamp meter around a single conductor.

Resistance (R) is the opposition a material offers to current flow. It is measured in ohms (Ω) with an ohmmeter on a de-energized, isolated circuit.

Ohm's Law

Georg Ohm showed that in a resistive circuit these three quantities are always related:

> V = I × R

Rearranged to solve for any unknown:

A simple memory aid is the Ohm's Law triangle: write V on top, I and R side by side below. Cover the unknown to read the formula.

Electrical Power

Power (P) is the rate at which a circuit converts electrical energy into heat, motion, or light. It is measured in watts (W).

> P = V × I

Combined with Ohm's Law, two additional forms are useful:

In HVAC/R, power ratings appear on compressor nameplates (often in kilowatts or horsepower) and on control transformers (in volt-amperes, VA).

Series and Parallel Circuits

Series circuits carry the same current through every component. Total resistance adds up: R_total = R1 + R2 + R3. Voltage divides across each resistor in proportion to its resistance. HVAC control boards often wire limit switches and safety switches in series so that any open switch stops the circuit.

Parallel circuits apply the same voltage across every branch. Total resistance is always less than the smallest branch resistor. Current divides among branches. Most 120 V and 240 V load circuits (motors, heaters) are wired in parallel so each device operates at full voltage.

Series-parallel circuits combine both arrangements. Solve them by simplifying the parallel sections first, then treat the result as a series circuit.

Applying Theory to HVAC/R Equipment

Compressor motor nameplates list full-load amperes (FLA) and voltage. You can verify that the supply voltage is correct and calculate the power the motor draws. If a 240 V compressor draws 15 A at full load, its power draw is P = 240 × 15 = 3,600 W (3.6 kW).

Control transformer sizing — A 24 V thermostat circuit is standard in residential and light-commercial HVAC. The transformer steps 120 V or 240 V down to 24 V AC. To choose the right transformer, add up the VA demand of every 24 V control device (thermostat, contactor coil, zone valves). The transformer's VA rating must meet or exceed that total. Because VA = V × I, a 40 VA transformer at 24 V can supply a maximum of about 1.67 A to the control circuit.

Meter Use and Safety

Always follow your employer's lockout/tagout (LOTO) procedures before opening any panel or handling components. Before taking any measurement on an energized circuit:

Percent error tells you how close your prediction was to the measured value:

> % error = |calculated − measured| ÷ calculated × 100

A result within ±5% confirms your understanding of the circuit. A larger error signals a wiring mistake, a faulty component, or a meter calibration issue.

Putting It Together

Ohm's Law and the power formula are not abstract math — they are the technician's first diagnostic tools. Before you touch a meter, calculate what the reading should be. If the meter agrees within ±5%, the circuit is behaving as designed. If it does not, you have found where to look next.

Key terms10

Voltage (V)Electrical pressure, measured in volts, that drives current through a circuit. Measured with a voltmeter connected in parallel.
Current (I)The flow of electrons through a conductor, measured in amperes (A). Measured in series with an ammeter or with a clamp meter around one conductor.
Resistance (R)Opposition to current flow, measured in ohms (Ω). Always measured on a de-energized, isolated circuit.
Ohm's LawThe relationship V = IR, which states that voltage equals current multiplied by resistance. Can be rearranged to find any one of the three quantities.
Power (P)The rate of energy conversion in a circuit, measured in watts (W). Calculated as P = V × I, P = I² × R, or P = V² ÷ R.
Series circuitA circuit in which all components share the same current path; total resistance is the sum of individual resistances; voltage divides across each component.
Parallel circuitA circuit in which each branch has the same voltage applied; total resistance is less than any single branch; current divides among branches.
Volt-amperes (VA)The unit used to rate transformer capacity in AC control circuits; numerically equal to volts multiplied by amperes in a purely resistive circuit.
Percent errorA measure of how closely a calculated (predicted) value matches a measured value: |calculated − measured| ÷ calculated × 100.
Full-load amperes (FLA)The current a motor draws when operating at its rated load and voltage, as listed on the nameplate; used to select wire size, overcurrent protection, and to verify normal operation.

Worked examples4

1. A 24 V control circuit has a contactor coil with a resistance of 40 Ω. What current flows through the coil, and what power does it consume?
  1. Identify knowns: V = 24 V, R = 40 Ω.
  2. Apply Ohm's Law to find current: I = V ÷ R = 24 ÷ 40 = 0.6 A.
  3. Apply the power formula: P = V × I = 24 × 0.6 = 14.4 W.
  4. Verify with the alternative formula: P = I² × R = (0.6)² × 40 = 0.36 × 40 = 14.4 W. ✓
Answer: Current = 0.6 A; Power = 14.4 W
2. A compressor operates at 240 V and draws 18 A at full load. What is its full-load power draw in watts and in kilowatts?
  1. Identify knowns: V = 240 V, I = 18 A.
  2. Calculate power: P = V × I = 240 × 18 = 4,320 W.
  3. Convert to kilowatts: 4,320 W ÷ 1,000 = 4.32 kW.
Answer: Full-load power = 4,320 W (4.32 kW)
3. A control board has two resistors in series: R1 = 220 Ω and R2 = 330 Ω, supplied by 12 V DC. Find total resistance, circuit current, and the voltage drop across each resistor.
  1. Find total resistance: R_total = R1 + R2 = 220 + 330 = 550 Ω.
  2. Find circuit current using Ohm's Law: I = V ÷ R_total = 12 ÷ 550 ≈ 0.02182 A (21.82 mA). The same current flows through both resistors.
  3. Find voltage drop across R1: V1 = I × R1 = 0.02182 × 220 ≈ 4.80 V.
  4. Find voltage drop across R2: V2 = I × R2 = 0.02182 × 330 ≈ 7.20 V.
  5. Verify: V1 + V2 = 4.80 + 7.20 = 12.00 V ✓ (equals supply voltage).
Answer: R_total = 550 Ω; I ≈ 21.82 mA; V1 ≈ 4.80 V; V2 ≈ 7.20 V
4. A 24 V thermostat control circuit powers three devices in parallel: a zone valve coil (48 Ω), a fan relay coil (60 Ω), and a humidistat coil (120 Ω). What is the total current the transformer must supply?
  1. In a parallel circuit, voltage across each branch equals the supply voltage: 24 V.
  2. Find branch current for each device using I = V ÷ R.
  3. Zone valve: I1 = 24 ÷ 48 = 0.50 A.
  4. Fan relay: I2 = 24 ÷ 60 = 0.40 A.
  5. Humidistat: I3 = 24 ÷ 120 = 0.20 A.
  6. Total current: I_total = 0.50 + 0.40 + 0.20 = 1.10 A.
  7. Total VA demand: P = V × I_total = 24 × 1.10 = 26.4 VA. A transformer rated at 40 VA would be adequate.
Answer: Total current = 1.10 A; Total VA demand = 26.4 VA

The math in this lesson2

Learners compute total resistance and current for series and parallel thermostat circuits.
A-SSE.1A-CED.4
Brush up in the math halls at newSchoolWorks.com:
In class: Lecture and worked examples: V = IR, P = VI, and their transpositions applied to compressor-motor nameplate data and control-transformer sizing for a 24 V thermostat circuit. · Students complete a 20-problem worksheet covering series, parallel, and series-parallel resistive circuits typical of HVAC control boards, self-checking with an answer key before instructor review. · Paired lab exercise: students build a simple resistive circuit on a breadboard, predict voltage drops across each resistor using Ohm's Law, then measure with a digital multimeter and record percent error.
Materials: Scientific calculators, HVAC/R electrical theory textbook (e.g., Refrigeration and Air Conditioning Technology, Tomczyk et al., current edition), breadboards, resistor assortment, 12 V DC power supply, digital multimeters, student worksheets
Check: Worksheet score ≥ 75% correct and breadboard measurements within ±5% of calculated values = pass. Students who score below 75% receive targeted re-teaching before the next lesson.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

Electrical Theory — Ohm's Law
1. A resistor in a 24 V control circuit has a resistance of 80 Ω. What current flows through it?
Electrical Measurement and Meters
2. A technician measures 118 V across a compressor contactor coil when 120 V is expected. The percent error between the calculated prediction (120 V) and the measured value (118 V) is closest to:
Electrical Theory — Circuit Types
3. Which of the following correctly states what happens to total resistance when a third resistor is added in parallel to an existing two-resistor parallel circuit?
Electrical Theory — Power Formula
4. A 240 V single-phase condensing unit draws 12 A at full load. What is the full-load power in kilowatts?
Control Transformers and 24 V Circuits
5. A technician needs to size a 24 V control transformer. The connected load consists of two relay coils, each rated 12 VA, and one zone valve rated 8 VA. What minimum transformer VA rating is required?
Electrical Safety and Test Instruments
6. When measuring resistance with a digital multimeter, the technician must ensure the circuit is:
Electrical Theory — Series Circuits
7. In a series control circuit, two safety switches (a high-pressure switch at 10 Ω and a low-pressure switch at 15 Ω) and a contactor coil at 50 Ω are connected across 24 V. What is the voltage drop across the contactor coil?
Electrical Theory — Power Formula
8. Which formula correctly calculates power when voltage is unknown but current and resistance are known?
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