Crash course: Voltage, amperage, and resistance basics with calculations (part 5)

Ohm's Law: the only equation you need first

Voltage (V) pushes current (I) through resistance (R). The relationship is V = I × R. Rearranged: I = V/R, R = V/I. Memorize it once, use it forever.

Voltage is measured in volts, current in amps, resistance in ohms. On a 120V circuit feeding a 12 ohm heating element, current draw is 120/12 = 10A. That circuit lands on a 15A breaker without trouble. Drop the resistance to 8 ohms and you pull 15A flat, which means nuisance trips on inrush.

Power follows from there: P = V × I, measured in watts. A 1500W space heater on 120V draws 12.5A. Same heater on 240V draws 6.25A. Half the current, half the conductor heating, half the voltage drop. That is why we feed big loads at higher voltages.

Voltage drop: the calc that saves callbacks

NEC 210.19(A) Informational Note 4 recommends branch circuit voltage drop stay under 3%, with a combined feeder and branch limit of 5%. It is not a hard rule, but inspectors and good foremen treat it as one.

For single phase, Vd = (2 × K × I × D) / CM. K is 12.9 for copper, 21.2 for aluminum. D is one-way distance in feet. CM is circular mils from Chapter 9 Table 8. For three phase, swap the 2 for 1.732.

• 120V circuit, 20A load, 100ft one-way, #12 copper (6530 CM): Vd = (2 × 12.9 × 20 × 100) / 6530 = 7.9V, or 6.6%. Fail.
• Same run on #10 copper (10380 CM): Vd = 4.97V, or 4.1%. Still over 3%.
• Bump to #8 copper (16510 CM): Vd = 3.12V, or 2.6%. Pass.

Long runs on small wire are the most common reason a motor hums and refuses to start, or LED drivers flicker at the end of a hallway. Size up before you pull, not after.

Resistance in the real world

Conductor resistance changes with length, cross section, material, and temperature. Copper has a temperature coefficient of about 0.00393 per degree C. A conductor sitting in a 50C attic has measurably higher resistance than the same wire in a 20C basement. That is why NEC 310.15(B) ambient correction factors exist.

Splices, terminations, and corroded lugs add resistance in series. A loose neutral at a panel can read fine cold and burn brown the moment a load comes on. If you see discoloration on a terminal, retorque per NEC 110.14(D) and inspect the conductor end. Cut and re-land if the strands are oxidized.

If a circuit reads correct voltage with no load but sags 10V under load, you have a high resistance connection somewhere upstream. Find it before something cooks.

Amperage, ampacity, and what the breaker actually protects

Amperage is current flow. Ampacity is what a conductor can carry continuously without exceeding its insulation rating. Per NEC Table 310.16, #12 THHN copper is rated 30A at 90C, but NEC 240.4(D) caps the overcurrent device at 20A for #12 copper. The breaker protects the wire, not the load.

Continuous loads (3 hours or more) require the circuit to be sized at 125% of the load per NEC 210.19(A)(1) and 210.20(A). A 16A continuous load needs a 20A breaker and conductors rated for 20A minimum. Miss this on a commercial lighting job and you will be back replacing tripped breakers within a month.

1. Identify load in amps.
2. If continuous, multiply by 1.25.
3. Apply ambient and bundling derates per NEC 310.15.
4. Pick conductor from Table 310.16 at the terminal temperature rating per NEC 110.14(C).
5. Pick OCPD per NEC 240.4 and 240.6.

Series vs parallel: where techs trip up

In series, resistances add: Rt = R1 + R2 + R3. Current is the same through every element, voltage divides. A bad bulb in an old series string kills the whole string.

In parallel, voltage is the same across each branch, current divides, and total resistance drops: 1/Rt = 1/R1 + 1/R2 + 1/R3. Two 240 ohm elements in parallel give 120 ohms, doubling the current draw at the same voltage. This is why adding receptacles to an existing circuit without recalculating load is how panels get overloaded.

Branch circuits in a residence are parallel from the panel out. Each device sees full voltage, and the breaker sees the sum of currents. Always sum your loads before adding to an existing circuit.

Measure resistance with the circuit dead and isolated. Ohmmeters inject their own voltage and will read garbage, or damage themselves, on a live conductor.

Field workflow for troubleshooting

When something is not working, walk the math before you start swapping parts. Measure voltage at the source, then at the load. Measure current under load. Compare to expected values from V = I × R.

• No voltage at source: open upstream, check OCPD and feeder.
• Voltage at source, none at load: open conductor or connection between.
• Voltage present, no current: open load or open neutral/ground return.
• Voltage sags hard under load: high resistance connection, undersized conductor, or failing source.
• Current higher than expected: shorted turns, parallel fault, or load drawing beyond nameplate.

Every electrical problem reduces to one of those five. Ohm's Law tells you which one before you open a single cover.