Ohm's Law + Power Formula for Trades Reference

Why this matters

Ohm's Law + power formula are the foundation of electrical work. Every multimeter reading, every breaker sizing, every motor diagnosis traces back to these relationships. The tech who's fluent in them diagnoses faster + sizes equipment correctly. This is the field card.

The four basic quantities

Voltage (V OR E): electrical pressure (volts)

• Pushes current through circuit
• Measured between two points
• Single-phase residential: 120V OR 240V

Current (I): electrical flow rate (amperes / amps)

• Quantity of electrons moving
• Measured in series (clamp meter most common)
• Determines wire size + breaker

Resistance (R): opposition to current (ohms / Ω)

• All conductors have some
• Heating elements + motor windings have specific resistance
• Measured with circuit de-energized

Power (P): rate of energy use (watts / W)

• Volts × amps for resistive loads
• Determines equipment capacity + utility bill
• Often kilowatts (kW = 1,000W)

Ohm's Law

E = I × R

Voltage equals current times resistance.

Rearranged:

• I = E ÷ R (current = voltage divided by resistance)
• R = E ÷ I (resistance = voltage divided by current)

Memorize one form; derive others.

Practical Ohm's Law examples

Heater element:

• Element resistance: 12Ω
• Supply voltage: 120V
• Current: I = 120 ÷ 12 = 10A

Verify reading:

• Element should draw 10A
• Reading higher = shorted (less resistance)
• Reading lower = open (more resistance)
• Reading zero = open circuit

Motor winding:

• Spec'd resistance: 8Ω
• Measured: 8.2Ω
• Within tolerance; winding OK

Spec'd: 8Ω; measured: 0.1Ω:

• Short circuit between windings
• Motor failure
• Replace

Spec'd: 8Ω; measured: infinite:

• Open winding
• Motor failure
• Replace

Power formula

P = E × I (for DC + resistive AC)

Power equals voltage times current.

For motors + reactive loads:

• P = E × I × PF (power factor)
• PF typically 0.7-0.95 for motors
• Reactive power separate calculation
• Most service calculation: E × I sufficient estimate

Rearranged:

• I = P ÷ E (current = power divided by voltage)
• E = P ÷ I (rarely used)

Practical power examples

Refrigerator:

• Nameplate 700W running
• Voltage: 120V
• Current: I = 700 ÷ 120 = ~5.8A

Verify amp draw:

• Clamp meter on cord
• Should read ~5.8A running
• Higher = motor straining (failing)

Water heater:

• 4500W element
• Voltage: 240V
• Current: I = 4500 ÷ 240 = 18.75A

Breaker size:

• 18.75A continuous load × 125% (NEC) = 23.4A
• 30A breaker minimum
• Code-compliant

AC condenser:

• Nameplate 3500W
• Voltage: 240V
• Current: I = 3500 ÷ 240 = ~14.6A

Combining Ohm's Law + Power

P = E² ÷ R OR P = I² × R

Useful for:

• Heater element wattage from resistance
• Heat generated in wire (I²R losses)
• Voltage drop calculations

Example: I²R losses:

• 50A current through wire
• 0.05Ω wire resistance (long run small gauge)
• Power lost as heat: 50² × 0.05 = 125W
• Significant; wire warms + voltage drops

Series circuit math

Resistors in series:

• Total resistance = sum
• R_total = R1 + R2 + R3

Current:

• Same through all (series circuit)

Voltage:

• Divides across each resistor proportionally

Example: Series christmas lights:

• 50 bulbs, each 2.4V
• Total = 120V
• One out = all out (open circuit)

Parallel circuit math

Resistors in parallel:

• Total resistance = 1 / (1/R1 + 1/R2 + 1/R3...)
• Always LESS than smallest resistor

Voltage:

• Same across all (parallel)

Current:

• Divides through branches inverse to resistance
• Lower resistance branch = more current

Example: Household circuit:

• All outlets parallel
• Each device sees 120V
• Each draws different current

Practical parallel example

Bedroom circuit:

• Lamp: 100W = 0.83A
• Phone charger: 5W = 0.04A
• TV: 80W = 0.67A
• Heater: 1500W = 12.5A

Total current: 0.83 + 0.04 + 0.67 + 12.5 = ~14A

On 15A circuit: near max; one more device could trip. On 20A circuit: comfortable margin.

AC vs DC

Ohm's Law applies to both:

• DC: straightforward
• AC: same for resistive loads (heaters)
• AC: more complex for motors / transformers (reactance)

For practical residential service:

• Resistive: heaters, incandescent, electric stove elements
• Inductive: motors, transformers, fluorescent ballasts
• Capacitive: certain loads, capacitor banks

Reactance + impedance

For inductive loads (motors):

• Inductive reactance (X_L) at AC frequency
• Adds to resistance
• Impedance (Z) = total opposition
• Z = √(R² + X_L²)

Practical implication:

• Motor draws more current than R alone suggests
• Power factor < 1
• Account in sizing

For typical residential: most service tech uses simple V × I × PF approximation.

Voltage drop

Common diagnostic + design concern:

Long wire run:

• Wire has resistance per foot
• Voltage drops along length
• At end of run, less voltage than source

Calculation:

• V_drop = I × R_wire
• R_wire = ρ × L ÷ A (resistivity × length / cross-section)

Practical rule:

• 3% maximum voltage drop typical
• 5% maximum branch + feeder combined

Example:

• 240V circuit, 50A load
• 100 ft run, 8 AWG copper
• 8 AWG: ~0.78Ω per 1000 ft
• Round trip 200 ft: 0.156Ω
• V_drop = 50 × 0.156 = 7.8V
• 7.8 ÷ 240 = 3.25% (just over limit)
• Consider larger wire

Wire ampacity

NEC tables:

• 14 AWG copper: 15A (60°C column for branch)
• 12 AWG: 20A
• 10 AWG: 30A
• 8 AWG: 40A (60°C); 50A (75°C)
• 6 AWG: 55A (60°C); 65A (75°C)
• 4 AWG: 70A (60°C); 85A (75°C)

Sizing logic:

• Calculate load
• Apply 125% for continuous
• Match wire to current
• Match breaker to wire

Heat dissipation

Power dissipated in wire = I² × R

• Heats wire
• Reduces ampacity if cluster
• Sometimes derate per NEC

Loose / corroded connection:

• Higher resistance
• More heat
• Eventually arc
• Fire risk

Tight connections matter.

Calculating amp draw for diagnosis

Compare measured to expected:

For element:

• Nameplate watts ÷ voltage = expected amps
• Measure with clamp meter
• Within ±10% = OK
• Higher = short (replace)
• Lower = open partial (replace)
• Zero = open complete (replace)

For motor:

• Nameplate FLA (Full Load Amps)
• Measure under load
• Higher than FLA = motor straining
• Lower = light load (sometimes OK)

Three-phase calculations

For commercial three-phase:

• P = E × I × 1.732 × PF
• 1.732 = √3 (square root of 3)
• Three-phase relationship

Example: 480V three-phase motor:

• 10 HP motor
• ~7,460W (746W per HP)
• Current per leg: I = 7460 ÷ (480 × 1.732 × 0.85) ≈ 10.5A
• Nameplate confirms

Power factor

For motors:

• Real power (kW) - useful work
• Apparent power (kVA) - what utility supplies
• Power factor = kW ÷ kVA

Lower PF:

• More current for same useful work
• Inefficient
• Commercial customers pay penalty

References

• NEC (National Electrical Code) ampacity tables
• IEEE electrical engineering references
• Standard electrical theory textbooks
• Manuall internal: Reading Wiring Schematics, Common Motor Diagnosis