Ohm's Law Wheel Calculator Guide: Voltage, Current, Resistance & Power

What Is Ohm's Law?

Ohm's Law is the fundamental relationship between voltage (V), current (I), and resistance (R) in an electrical circuit. Published by Georg Simon Ohm in 1827, it states:

V = I × R

Voltage (measured in volts) is the "pressure" pushing electrons through a conductor. Current (measured in amperes) is the flow rate of electrons. Resistance (measured in ohms, symbolized Ω) is how much the conductor opposes that flow.

Think of it like water in a pipe. Voltage is the water pressure, current is the flow rate, and resistance is how narrow the pipe is. According to the National Institute of Standards and Technology (NIST), the ohm is defined so precisely that it can be reproduced to within 1 part in 10 billion using the quantum Hall effect.

The Ohm's Law Power Wheel: All 12 Formulas

The power wheel combines Ohm's Law (V = IR) with the power equation (P = VI) to produce 12 formulas. Given any two of the four quantities — voltage (V), current (I), resistance (R), power (P) — you can calculate the other two.

Voltage (V) Formulas

Current (I) Formulas

Resistance (R) Formulas

Power (P) Formulas

Real-World Circuit Examples

Example 1: LED Resistor Sizing

You want to run a standard red LED (2V forward voltage, 20mA rated current) from a 5V Arduino pin. What resistor do you need?

Voltage across resistor = 5V – 2V = 3V
R = V ÷ I = 3V ÷ 0.020A = 150Ω
Power dissipated: P = V × I = 3V × 0.020A = 0.06W. A standard 1/4W resistor works fine.

Example 2: Household Circuit Load

Can you run a 1,500W space heater and a 300W TV on the same 15A circuit?

Total power = 1,800W. Current = P ÷ V = 1,800 ÷ 120 = 15A. That maxes out the breaker. The NEC 80% continuous load rule (Article 210.20) says you should not exceed 12A (1,440W) on a 15A circuit for sustained loads. The answer: no, not safely. The U.S. Consumer Product Safety Commission reports that overloaded circuits cause an estimated 47,700 home fires annually.

Example 3: Car Audio Amplifier

A 500W car amplifier runs on a 14.4V system. How much current does it draw?

I = P ÷ V = 500 ÷ 14.4 = 34.7A. That's why car audio amplifiers need thick power cables — 4 AWG wire is rated for about 40A. According to the American Wire Gauge standard, using undersized wire causes voltage drop and heat buildup.

Series vs. Parallel Resistor Circuits

How resistors are connected affects total resistance and current flow.

Two 100Ω resistors in series = 200Ω. The same two in parallel = 50Ω. This is why parallel circuits draw more current — lower total resistance means higher current for the same voltage (I = V/R).

Common Wire Sizes and Current Ratings

Choosing the right wire gauge is a direct application of Ohm's Law. Thinner wire has higher resistance, causing voltage drop and heat.

The NEC (NFPA 70, Table 310.16) defines ampacity ratings for copper conductors at 60°C, 75°C, and 90°C insulation temperatures. The values above are for 60°C-rated insulation — the most conservative and common in residential wiring.

Frequently Asked Questions

What is Ohm's Law in simple terms?

Ohm's Law states that voltage equals current times resistance (V = I × R). If you know any two of voltage, current, or resistance, you can calculate the third. A 12V battery pushing current through a 4Ω resistor produces 3 amps (12 ÷ 4 = 3).

What are all 12 formulas on the Ohm's Law wheel?

The wheel gives 3 formulas each for voltage (V = IR, V = P/I, V = √(PR)), current (I = V/R, I = P/V, I = √(P/R)), resistance (R = V/I, R = P/I², R = V²/P), and power (P = VI, P = I²R, P = V²/R). All 12 derive from just two relationships: V = IR and P = VI.

How do you calculate power dissipation in a resistor?

Use P = I²R or P = V²/R. A 100Ω resistor with 0.5A flowing through it dissipates P = (0.5)² × 100 = 25 watts. Standard through-hole resistors are rated for 0.25W, so you would need a power resistor rated for at least 25W. Exceeding a resistor's power rating causes overheating and fire risk.

What is the difference between AC and DC for Ohm's Law?

Ohm's Law applies directly to DC circuits. In AC circuits, replace resistance (R) with impedance (Z), giving V = IZ. Impedance includes resistance plus capacitive and inductive reactance. For purely resistive AC loads — incandescent bulbs, space heaters — the math is identical to DC.

How many watts can a 15-amp household circuit handle?

P = V × I = 120V × 15A = 1,800 watts maximum. But the National Electrical Code (NEC Article 210.20) requires circuits be loaded to no more than 80% for continuous loads, so the practical limit is 1,440 watts. A 20-amp circuit handles up to 2,400W (1,920W at 80%).