Electronics for Beginners: Ohm's Law, Voltage Drop, and Power Calculations

You are wiring a 20-amp circuit for a workshop. The run is 150 feet from the panel. You grab 12 AWG wire because that is what 20-amp circuits use. You connect everything, turn on the breaker, and your table saw struggles to start. The lights dim when it does. What went wrong?

The answer is voltage drop. At 150 feet, 12 AWG copper wire loses enough voltage that your saw is getting 108 volts instead of 120. The National Electrical Code recommends keeping voltage drop under 3% on branch circuits, and you are at 6.2%. You need larger wire.

Electronics and electrical work come down to three core formulas: Ohm's Law, voltage drop, and power. Master these and you can size wires, calculate loads, troubleshoot circuits, and understand why your devices behave the way they do.

Ohm's Law: The Foundation

Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R). It states that current equals voltage divided by resistance.

V = I x R

From this one equation, you can derive three forms:

• V = I x R (find voltage)
• I = V / R (find current)
• R = V / I (find resistance)

Example: LED Circuit

You want to power an LED that requires 2 volts at 20 milliamps (0.02 amps) from a 9-volt battery. What resistor do you need?

The resistor must drop the excess voltage: 9V - 2V = 7V. Current through the LED: 0.02A. Resistance = 7V / 0.02A = 350 ohms.

Use the next standard value up: 360 ohms (or 390 ohms if you want to be safe).

Use our Ohm's Law Calculator to calculate voltage, current, resistance, or power from any two known values.

Power Calculation

Electrical power (in watts) is the rate at which electrical energy is transferred. The basic formula:

P = V x I

Combined with Ohm's Law, you get two additional forms:

• P = I^2 x R (power from current and resistance)
• P = V^2 / R (power from voltage and resistance)

Example: Resistor Power Rating

In the LED circuit above, the resistor drops 7V at 0.02A. Power dissipated by the resistor: P = 7 x 0.02 = 0.14 watts. A standard 1/4 watt (0.25W) resistor is sufficient.

If you used a 100-ohm resistor instead: P = 7^2 / 100 = 0.49 watts. A 1/4 watt resistor would overheat and fail. You would need a 1/2 watt or 1 watt resistor.

Electricity Cost Calculation

To calculate how much an appliance costs to run:

Cost = (Watts x Hours x Rate per kWh) / 1000

A 1,500-watt space heater running 8 hours per day at $0.16/kWh: (1,500 x 8 x 0.16) / 1000 = $1.92 per day. Over a month: $57.60.

Use our Electricity Calculator to calculate power consumption and cost for any appliance.

Voltage Drop: Why Wire Size Matters

Voltage drop is the reduction in voltage that occurs along a conductor due to its resistance. The longer the wire, the more voltage is lost. This is why wire size matters for long runs.

The Voltage Drop Formula

For single-phase and DC circuits:

Vd = (2 x L x I x R) / 1000

Where:

• Vd = voltage drop in volts
• L = one-way length in feet
• I = load current in amps
• R = conductor resistance in ohms per 1,000 feet

For three-phase circuits, replace the 2 with 1.732 (square root of 3).

NEC Conductor Resistance Values (2026)

These are DC resistance values for copper conductors at 75 degrees C, from NEC Chapter 9, Table 8:

Wire Size	Copper (ohms/1,000 ft)	Aluminum (ohms/1,000 ft)
14 AWG	3.14	Not permitted
12 AWG	1.98	3.25
10 AWG	1.24	2.04
8 AWG	0.778	1.28
6 AWG	0.491	0.808
4 AWG	0.308	0.508
2 AWG	0.194	0.319
1/0 AWG	0.122	0.201
4/0 AWG	0.0608	0.100

Source: NFPA 70-2026, Chapter 9, Table 8.

NEC Voltage Drop Recommendations

The NEC recommends (in informational notes, not mandatory requirements):

• Maximum 3% voltage drop on branch circuits
• Maximum 5% total (feeder plus branch combined)

Most inspectors treat these as de facto requirements. Exceeding 3% on a branch circuit will likely fail inspection.

Example: The Workshop Circuit

Back to our 20-amp workshop circuit, 150 feet from the panel, using 12 AWG copper wire.

Vd = (2 x 150 x 20 x 1.98) / 1000 = 11.88 volts. Percentage drop: 11.88 / 120 = 9.9%.

That is way too high. The NEC recommends 3% maximum, which is 3.6 volts on a 120V circuit.

To stay under 3%, you need lower resistance wire. Try 10 AWG (1.24 ohms/1,000 ft): Vd = (2 x 150 x 20 x 1.24) / 1000 = 7.44 volts = 6.2%. Still too high.

Try 8 AWG (0.778 ohms/1,000 ft): Vd = (2 x 150 x 20 x 0.778) / 1000 = 4.67 volts = 3.9%. Close but still over.

Try 6 AWG (0.491 ohms/1,000 ft): Vd = (2 x 150 x 20 x 0.491) / 1000 = 2.95 volts = 2.46%. Under 3%.

For a 150-foot, 20-amp circuit, you need 6 AWG copper wire to stay within NEC recommendations. That is two wire sizes larger than the 12 AWG most people would use.

Use our Voltage Drop Calculator to calculate voltage drop for any circuit length, wire size, and load.

Resistor Color Codes

Resistors use colored bands to indicate their resistance value and tolerance. The 4-band system is most common.

Color	Digit	Multiplier	Tolerance
Black	0	x1
Brown	1	x10	1%
Red	2	x100	2%
Orange	3	x1,000
Yellow	4	x10,000
Green	5	x100,000	0.5%
Blue	6	x1,000,000	0.25%
Violet	7		0.1%
Gray	8		0.05%
White	9
Gold		x0.1	5%
Silver		x0.01	10%

Reading a 4-Band Resistor

A resistor with bands Yellow, Violet, Orange, Gold:

• Yellow = 4 (first digit)
• Violet = 7 (second digit)
• Orange = x1,000 (multiplier)
• Gold = 5% (tolerance)

Value = 47 x 1,000 = 47,000 ohms = 47k ohms, with 5% tolerance. Actual resistance is between 44,650 and 49,350 ohms.

Use our Resistor Calculator to decode resistor color bands and calculate resistance values.

Real-World Scenarios

Scenario 1: Sizing a Water Heater Circuit

You are installing a 4,500-watt, 240-volt electric water heater. The circuit is 80 feet from the panel.

Current: I = P / V = 4,500 / 240 = 18.75 amps. Required wire size (NEC 310.16): 12 AWG copper is rated for 20 amps at 75C. But 18.75 amps is close to the 20-amp rating. Use 10 AWG (30 amps) for safety margin.

Voltage drop with 10 AWG at 80 feet: Vd = (2 x 80 x 18.75 x 1.24) / 1000 = 3.72 volts = 1.55%. Under 3%. Acceptable.

Scenario 2: LED Strip Lighting

You want to install a 16-foot LED strip that draws 1.5 amps at 12V. The power supply is 20 feet away.

Voltage drop with 18 AWG wire (approximately 6.39 ohms/1,000 ft): Vd = (2 x 20 x 1.5 x 6.39) / 1000 = 0.38 volts = 3.2%. Slightly over 3%.

At 11.62V, your LED strip will be noticeably dimmer at the far end. Use 16 AWG wire (approximately 4.02 ohms/1,000 ft): Vd = (2 x 20 x 1.5 x 4.02) / 1000 = 0.24 volts = 2.0%. Acceptable.

Scenario 3: Calculating Appliance Energy Cost

Your window AC unit draws 1,200 watts. You run it 10 hours per day during summer (90 days).

Daily cost: (1,200 x 10 x 0.16) / 1000 = $1.92 Seasonal cost: $1.92 x 90 = $172.80

If you switch to a more efficient unit that draws 800 watts: Daily cost: (800 x 10 x 0.16) / 1000 = $1.28 Seasonal cost: $1.28 x 90 = $115.20 Savings: $57.60 per summer

Common Mistakes

1. Using wire that is too small for long runs. The NEC ampacity tables tell you the minimum wire size for the current, but they do not account for voltage drop on long runs. Always calculate voltage drop separately for runs over 50 feet.

2. Forgetting the return path. The voltage drop formula multiplies by 2 because current travels out and back. The one-way length is used in the formula, but the factor of 2 accounts for the round trip.

3. Undersizing resistor power ratings. A resistor that dissipates 0.4 watts will overheat and fail if rated for only 0.25 watts. Always calculate power dissipation and choose a resistor rated for at least 2x the expected dissipation.

4. Mixing up AC and DC calculations. The voltage drop formula is the same for single-phase AC and DC. For three-phase AC, use 1.732 instead of 2. Do not mix them up.

5. Ignoring temperature effects. Conductor resistance increases with temperature. NEC Table 8 values are at 75 degrees C. In hot environments (attics, near furnaces), resistance is higher and voltage drop is worse.

External Research and Resources

• NFPA 70: National Electrical Code (NEC) is the authoritative source for all U.S. electrical installation requirements, including conductor ampacity tables (Article 310) and voltage drop recommendations (Article 210.19 informational notes).
• All About Circuits: Ohm's Law Tutorial provides free, comprehensive electronics education including worked examples of Ohm's Law applications.
• NIST: Electrical Reference Standards maintains the national measurement standards for electrical quantities used in calibration and testing.

People Also Ask

What is Ohm's Law and how do I use it?

Ohm's Law states that voltage equals current times resistance (V = I x R). If you know any two of these values, you can calculate the third. For example, if a circuit has 12V across a 240-ohm resistor, the current is 12 / 240 = 0.05 amps (50 milliamps).

How do I calculate voltage drop?

For single-phase or DC circuits: Vd = (2 x Length x Current x Resistance) / 1000, where resistance is in ohms per 1,000 feet from NEC Table 8. For three-phase, replace 2 with 1.732. The NEC recommends keeping voltage drop under 3% for branch circuits and 5% total. Use our Voltage Drop Calculator for instant results.

What size wire do I need for a 20-amp circuit?

The minimum wire size for a 20-amp circuit is 12 AWG copper per NEC Table 310.16. However, for runs longer than 50 feet, you may need larger wire to keep voltage drop under 3%. At 150 feet, you may need 6 AWG or 8 AWG depending on the load. Always calculate both ampacity and voltage drop.

How much does it cost to run an appliance?

Cost = (Watts x Hours x Rate per kWh) / 1000. A 1,500-watt heater running 8 hours at $0.16/kWh costs (1,500 x 8 x 0.16) / 1000 = $1.92 per day. Use our Electricity Calculator for any appliance.

Related Calculators

• Ohm's Law Calculator - Calculate voltage, current, resistance, or power
• Voltage Drop Calculator - Calculate voltage drop for any wire size and length
• Resistor Calculator - Decode resistor color bands and calculate values
• Electricity Calculator - Calculate power consumption and energy cost
• Horsepower Calculator - Calculate horsepower from torque and RPM
• Power Calculator - Calculate electrical power from voltage and current