The term "pie chart" in electrical theory almost always refers to the Ohm's Law Wheel (or Formula Wheel). It is a circular reference diagram divided into four quadrants—Power (P), Current (I), Voltage (E or V), and Resistance (R)—containing 12 distinct formulas. If you know any two variables in a DC circuit, the wheel gives you the exact formula to find the other two. Below is the complete translation of that wheel into a searchable, decision-forward reference table, along with the AC modifiers and bench scenarios you actually need.
The Ohm's Law Pie Chart: Complete Formula Lookup Table
How to read this table: Locate the Target Variable you need to find in the first column. Read across to the Known Variables column to match the two values you currently have on your multimeter or schematic. The Formula column provides the exact math. All base formulas assume pure DC or purely resistive AC loads. Standard symbol conventions follow IEEE Std 100 and standard DC textbook conventions, where Voltage is denoted as either V or E (Electromotive Force).
| Target Variable | Known Variables | Formula | Units |
|---|---|---|---|
| Current (I) | Voltage (V), Resistance (R) | I = V / R | Amperes (A) |
| Power (P), Voltage (V) | I = P / V | Amperes (A) | |
| Power (P), Resistance (R) | I = √(P / R) | Amperes (A) | |
| Voltage (V) | Current (I), Resistance (R) | V = I × R | Volts (V) |
| Power (P), Current (I) | V = P / I | Volts (V) | |
| Power (P), Resistance (R) | V = √(P × R) | Volts (V) | |
| Resistance (R) | Voltage (V), Current (I) | R = V / I | Ohms (Ω) |
| Voltage (V), Power (P) | R = V² / P | Ohms (Ω) | |
| Power (P), Current (I) | R = P / I² | Ohms (Ω) | |
| Power (P) | Voltage (V), Current (I) | P = V × I | Watts (W) |
| Current (I), Resistance (R) | P = I² × R | Watts (W) | |
| Voltage (V), Resistance (R) | P = V² / R | Watts (W) |
Decision Path: Which Formula Quadrant to Use
When troubleshooting or designing, you rarely sit down and say, "I need to use the P = I²R formula." Instead, you look at the physical components and measurement tools in front of you. Use this decision tree to terminate on the exact formula and component action required.
| If your physical scenario is... | And you are holding/measuring... | Then use this Formula | Terminating Action / Pick |
|---|---|---|---|
| Sizing a fuse or breaker for a new DC load | Load wattage (nameplate) and system voltage | I = P / V | Pick a fuse rated 125% of the calculated I (e.g., calc 8A → buy 10A fuse). |
| Checking if a resistor will overheat on a breadboard | Measured voltage drop across the resistor and its color-code resistance | P = V² / R | If P > 0.25W, swap the 1/4W resistor for a 1/2W or 1W metal film part. |
| Finding an unknown short circuit on a PCB trace | Injected known test current (via bench supply) and measured mV drop | R = V / I | If R < 1Ω, probe downstream with a thermal camera to find the hot short. |
| Sizing a current-limiting resistor for a standard 5mm LED | Source voltage, LED forward voltage (Vf), and target current (usually 20mA) | R = (Vsource - Vf) / I | Calculate R, then pick the next highest standard E12 series resistor value. |
AC vs. DC: How Power Factor Modifies the Base Values
The standard Ohm's Law pie chart assumes a purely resistive DC circuit (or an AC circuit with a power factor of 1.0, like a basic heating element). When you introduce inductive or capacitive loads in AC systems—such as motors, transformers, or switching power supplies—the base Power (P) formulas must be modified by the Power Factor (PF).
Worked Numeric Example:
You are wiring a 120V AC induction motor. Your clamp meter reads 10A of current draw. The motor's nameplate lists a Power Factor (PF) of 0.80.
Incorrect DC Pie Chart Math: P = 120V × 10A = 1200W.
Correct AC Modified Math: P = 120V × 10A × 0.80 = 960W (True Power).
If you sized your cooling system or solar inverter based on the unmodified pie chart formula, you would overestimate the real work the motor is doing by 25%, though you must still size the wire and breaker for the full 10A of apparent current.
What the Pie Chart Cannot Tell You (And How to Fix It)
The Ohm's Law wheel is a mathematical truth, but it is blind to physical reality. Here is what the table cannot tell you, and the standards you must consult instead:
- Wire Ampacity and Thermal Limits: The wheel will tell you that a 12V system drawing 120W requires 10A (I = P/V). It will not tell you what size wire to use. For that, you must consult NEC Table 310.16 (or your local equivalent) to ensure the wire insulation can handle the heat at 10A without melting.
- Voltage Drop over Distance: V = I × R applies to the load, but copper wire has its own resistance. Over a 50-foot run, the voltage at the load will be lower than the source. You must calculate the wire's specific resistance (e.g., 14 AWG copper is ~2.525 Ω per 1000 ft) and subtract that drop from your source V.
- RMS vs. Peak Voltage: If you measure an AC sine wave with an oscilloscope, the peak voltage of a standard 120V US outlet is actually ~170V. The pie chart formulas for AC power require the RMS (Root Mean Square) voltage (120V), not the peak voltage. If you only have the peak value, divide it by √2 (1.414) before plugging it into the wheel.
Quick-Jump Bookmark Rows for Common Bench Scenarios
Bookmark these three specific derivations. They account for 90% of the daily calculations performed at an electronics workbench.
Scenario 1: Sizing an LED Current-Limiting Resistor
The Setup: You have a 9V battery, a standard red LED (Vf = 2.0V), and you want to limit current to 20mA (0.02A) to prevent the LED from burning out.
The Formula: R = (Vsource - Vf) / I
The Math: R = (9V - 2.0V) / 0.02A = 7V / 0.02A = 350Ω.
Terminating Pick: 350Ω is not a standard E12 value. Pick the next highest standard value: 390Ω 1/4W resistor.
Scenario 2: Calculating MOSFET Heat Dissipation
The Setup: You are switching a 5A DC motor using an IRLZ44N MOSFET. You need to know if it needs a heatsink.
The Formula: P = I² × Rds(on)
The Math: The datasheet lists Rds(on) at roughly 0.022Ω (with 5V gate drive). P = (5A)² × 0.022Ω = 25 × 0.022 = 0.55W.
Terminating Pick: A standard TO-220 package dissipates about 1W to 1.5W in free air before getting too hot to touch. At 0.55W, no heatsink is required, but ensure adequate PCB copper pour for ventilation.
Scenario 3: Finding Max Current for a 1/4W Resistor
The Setup: You have a 1kΩ (1000Ω) resistor on hand, and you need to know the absolute maximum current you can push through it before it exceeds its 1/4W (0.25W) thermal rating and fails.
The Formula: I = √(P / R)
The Math: I = √(0.25W / 1000Ω) = √(0.00025) = 0.0158A.
Terminating Pick: The maximum safe continuous current is 15.8 mA. If your circuit demands 20mA, you must swap to a 1/2W resistor or a lower resistance value.
