4.4 Basic Electricity, Ohm's Law & Electrical Power for HVAC

4.4 Basic Electricity, Ohm's Law & Electrical Power for HVAC

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The Four Quantities

Ohm's Law

$$E = I \times R \qquad I = \frac{E}{R} \qquad R = \frac{E}{I}$$

The Power Wheel

$$P = E \times I \qquad P = I^2 \times R \qquad P = \frac{E^2}{R}$$

Worked example: a 240-volt electric heating element measures 9.6 ohms.

• Current: $I = 240 / 9.6 = 25\text{ A}$
• Power: $P = 240 \times 25 = 6{,}000\text{ W} = 6\text{ kW}$
• Heat output: $6\text{ kW} \times 3{,}412 = 20{,}472\text{ Btu/h}$

The constant 3,412 Btu/h per kilowatt is worth memorizing; it converts any electric resistance heat rating to a thermal load and appears repeatedly on the exam.

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Series and Parallel Circuits

Series

One path. The same current flows through every component, resistances add, and voltage divides in proportion to resistance.

$$R_T = R_1 + R_2 + R_3 \qquad I_T = I_1 = I_2 = I_3$$

Safety devices are wired in series with the load precisely so that opening any one of them stops all current - the high-limit switch, rollout switch, pressure switch, and door switch on a furnace form a series safety string.

Parallel

Multiple paths. Every branch sees the same voltage, currents add, and total resistance is always less than the smallest branch resistance.

$$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \qquad I_T = I_1 + I_2 + I_3$$

Loads - contactor coils, transformers, blower motors, condenser fan motors - are wired in parallel so that each receives full voltage and any one can operate independently.

Two-resistor shortcut: $R_T = \dfrac{R_1 \times R_2}{R_1 + R_2}$. Two 20-ohm branches in parallel give $400 / 40 = 10$ ohms.

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Alternating Current, Phase and Power Factor

• North American utility power alternates at 60 hertz - the sine wave completes 60 full cycles per second, reversing polarity 120 times.
• Meters read root-mean-square (RMS) values. A nominal 240 V RMS sine wave has a peak of $240 \times 1.414 = 339$ V, which is why a 240-volt circuit stresses insulation to roughly 340 volts.
• Single-phase residential service is normally 120/240 V; three-phase commercial service is commonly 208Y/120 V, 480Y/277 V, or 240 V delta.

Power in AC Circuits

Purely resistive loads such as electric heat have a power factor of 1.0, so watts equal volt-amperes. Motors are inductive: current lags voltage and the power factor falls to roughly 0.80 to 0.90, so a motor drawing 10 A at 240 V consumes 2,400 VA but only about 2,040 watts of true power.

Three-phase example: a 480-volt, three-phase compressor draws 22 A at a 0.85 power factor.

$$P = 1.732 \times 480 \times 22 \times 0.85 = 15{,}549\text{ watts} \approx 15.5\text{ kW}$$

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Voltage Unbalance: A Motor Killer

Three-phase voltage unbalance produces disproportionate current unbalance and rapid winding heating.

$$\%\text{ Unbalance} = \frac{\text{Maximum deviation from average voltage}}{\text{Average voltage}} \times 100$$

Worked example: measured line voltages are 462, 476, and 469 V. The average is $(462 + 476 + 469)/3 = 469$ V. The maximum deviation is $476 - 469 = 7$ V. Unbalance is $7 / 469 \times 100 = 1.49\%$.

• NEMA recommends operating motors at no more than 1% voltage unbalance.
• Current unbalance runs roughly 6 to 10 times the voltage unbalance percentage.
• At 2% voltage unbalance a motor should be derated; at 5% it should not be operated at all.

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Measuring Safely

• Voltage is measured in parallel with the circuit, under power. Resistance is measured only with power off and with capacitors discharged - an ohmmeter applied to a live circuit is destroyed and can injure the technician.
• A clamp ammeter reads the magnetic field around a single conductor. Clamping both conductors of a 240-volt circuit reads zero, because the opposing fields cancel.
• Meter category (CAT) ratings describe how much transient energy the meter can survive: CAT II at the receptacle, CAT III at the distribution panel and fixed equipment, CAT IV at the service entrance and utility connection. Use a CAT III 600 V or better meter at HVAC disconnects and panels, and confirm the leads carry the same rating as the meter.
• Always apply the live-dead-live test: prove the meter on a known live source, test the target circuit, then prove the meter again.