Trades Math Basics: Ohm’s Law (E = I × R, P = E × I – Voltage, Current, Resistance, Power)

Trades Math – Ohm’s Law (E = I × R, P = E × I – Voltage, Current, Resistance, Power)

(For Electricians, HVAC Techs, and Apprentices Prepping for Licensing Exams)

What This Is

Ohm’s Law (E = I × R) and the power formula (P = E × I) are the foundation of electrical work. You’ll use them daily to: - Size wires and breakers (e.g., "This 240V motor pulls 12A—what’s the minimum wire gauge?"). - Troubleshoot circuits (e.g., "Why’s this 120V outlet only reading 108V? Is the wire too thin or the load too high?"). - Calculate power consumption (e.g., "How much will this 5kW electric heater add to the customer’s bill?"). - Pass your licensing exam (most states test Ohm’s Law in multiple-choice and load-calculation problems).

Real-world scenario: You’re wiring a 240V baseboard heater rated at 3,840W. The nameplate says "16A," but the circuit breaker keeps tripping. Is the breaker undersized, or is there a wiring issue? (Spoiler: You’ll solve this in the Step-by-Step section.)

Key Terms & Formulas

• Voltage (E or V): Electrical "pressure" pushing current through a wire. Measured in volts (V). Example: A 120V outlet has enough "push" to power a light bulb but not a 240V dryer.

• Current (I): Flow of electrons, measured in amperes (amps, A). Example: A 15A circuit breaker trips if the current exceeds 15A.

• Resistance (R): Opposition to current flow, measured in ohms (?). Example: A long, thin wire has higher resistance than a short, thick one (like a garden hose vs. a fire hose).

• Power (P): Work done by electricity, measured in watts (W) or kilowatts (kW). Example: A 1,500W hair dryer uses more power than a 60W light bulb.

• Ohm’s Law: E = I × R (Voltage = Current × Resistance). Example: If a circuit has 10A and 12?, the voltage is 10A × 12? = 120V.

• Power Formula: P = E × I (Power = Voltage × Current). Example: A 120V circuit with 10A draws 120V × 10A = 1,200W (1.2kW).

• Watts to Amps (for 120V): I = P ÷ E-Amps = Watts ÷ 120V. Example: A 600W tool on a 120V circuit draws 600W ÷ 120V = 5A.

• Watts to Amps (for 240V): I = P ÷ E-Amps = Watts ÷ 240V. Example: A 3,840W heater on 240V draws 3,840W ÷ 240V = 16A.

• Resistance of a Wire: R = (K × L) ÷ CM (K = resistivity, L = length in feet, CM = circular mils). Example: 100 ft of #12 copper wire (K = 12.9, CM = 6,530) has R = (12.9 × 100) ÷ 6,530-0.2?.

• Voltage Drop: VD = I × R (Voltage drop = Current × Wire resistance). Example: If a 10A load flows through 0.2? wire, VD = 10A × 0.2? = 2V drop (120V-118V at the load).

• NEC 80% Rule: Continuous loads (3+ hours) must be ?80% of breaker rating. Example: A 20A breaker can only handle 20A × 0.8 = 16A continuous load.

Step-by-Step / Process Flow

How to Solve Any Ohm’s Law or Power Problem

1. Identify what you know and what you need to find.

2. Example: You know P = 3,840W and E = 240V. You need I (current) to size the breaker.

3. Pick the right formula.

4. Need current (I)? Use I = P ÷ E or I = E ÷ R.
5. Need power (P)? Use P = E × I.

6. Need resistance (R)? Use R = E ÷ I.

7. Plug in the numbers and solve.

8. Example: I = 3,840W ÷ 240V = 16A.

9. Apply code rules (NEC 80% rule for breakers).

10. Example: 16A continuous load-16A ÷ 0.8 = 20A breaker minimum.

11. Check for voltage drop (if wire run is long).

12. Example: 100 ft of #12 wire has R-0.2?. VD = 16A × 0.2? = 3.2V drop (240V-236.8V at the heater).

13. NEC max drop: 3% for branch circuits-240V × 0.03 = 7.2V max. 3.2V is OK.

14. Verify your answer makes sense.

15. Example: A 16A heater on a 20A breaker? Yes (16A-20A × 0.8).
16. A 16A heater on a 15A breaker? No (16A > 15A × 0.8 = 12A).

Common Mistakes

• Mistake: Forgetting the 80% rule for continuous loads.
• Correction: Always multiply the breaker rating by 0.8 for loads running 3+ hours.

• Why? Breakers can overheat if run at 100% capacity for long periods.

• Mistake: Mixing up watts and amps in calculations.

• Correction: Use P = E × I to convert between them.

• Why? A 1,500W tool on 120V draws 12.5A, not 1,500A!

• Mistake: Ignoring voltage drop on long wire runs.

• Correction: Calculate VD = I × R and ensure it’s ?3% of supply voltage.

• Why? Too much drop causes motors to overheat and lights to dim.

• Mistake: Using the wrong wire gauge for the current.

• Correction: Check NEC Table 310.16 (e.g., #12 wire = 20A max, #10 wire = 30A max).

• Why? Undersized wire can overheat and start fires.

• Mistake: Assuming 240V loads draw half the current of 120V loads.

• Correction: Power (P) is the same—only current changes. A 1,200W load draws 10A at 120V but 5A at 240V.
• Why? P = E × I-If voltage doubles, current halves for the same power.

Trade-Specific Insights

Field Trick: Use a clamp meter to measure current, then calculate power. - Example: Clamp a wire and read 8A at 240V-P = 240V × 8A = 1,920W.

Code Requirement: NEC 210.19(A) says wire must handle 125% of continuous loads. - Example: A 16A continuous load needs 16A × 1.25 = 20A wire (use #12 for 20A circuits).

Shortcut for Breaker Sizing: - Non-continuous loads: Breaker-load current. - Continuous loads: Breaker-load current ÷ 0.8.

Voltage Drop Cheat: - For 120V circuits, VD = (2 × I × L) ÷ 1,000 (for copper wire). Example: 10A, 100 ft run-VD = (2 × 10 × 100) ÷ 1,000 = 2V drop.

Quick Check Questions

1. A 240V water heater draws 18A. What’s its power rating?
2. Answer: 4,320W (P = 240V × 18A).

3. Why? Power = Voltage × Current.

4. You measure 115V at a 120V outlet with a 10A load. What’s the wire resistance?

5. Answer: 0.5? (E = I × R-5V drop = 10A × R-R = 0.5?).

6. Why? Voltage drop = Current × Resistance.

7. A 5kW electric range runs on 240V. What’s the minimum breaker size (continuous load)?

8. Answer: 26A (I = 5,000W ÷ 240V = 20.83A-20.83A ÷ 0.8 = 26A-Next standard breaker = 30A).
9. Why? Continuous loads need 125% of current.

Last-Minute Cram Sheet

1. Ohm’s Law: E = I × R (Volts = Amps × Ohms).
2. Power Formula: P = E × I (Watts = Volts × Amps).
3. Watts to Amps (120V): I = P ÷ 120.
4. Watts to Amps (240V): I = P ÷ 240.
5. NEC 80% Rule: Continuous loads-80% of breaker rating.
6. Voltage Drop: VD = I × R (Keep ?3% of supply voltage).
7. Wire Gauge (NEC Table 310.16):

8. 14 = 15A, #12 = 20A, #10 = 30A, #8 = 40A.

9. Continuous Loads: Breaker-Load ÷ 0.8.
10. Voltage Drop Cheat: VD = (2 × I × L) ÷ 1,000 (for 120V copper).
11. Power Factor: For motors, P = E × I × PF (PF-0.8 for most motors).