Ohm's Law and the Power Equations
Ohm's Law relates the three fundamental quantities in any electrical circuit: voltage (V), current (I), and resistance (R). Combined with the power equation, these four variables - V, I, R, and P - are linked by 12 formulas that let you solve any circuit problem if you know any two of them.
The Core Formulas
V=I×R
P=V×I
From these two equations, any other relationship can be derived by substitution. For example, P = I2 * R comes from replacing V with I*R in the power formula.
All 12 Derived Formulas
| To Find | Given V, I | Given V, R | Given I, R | Given P + one |
|---|---|---|---|---|
| Voltage | - | - | I x R | P/I or √(P*R) |
| Current | - | V/R | - | P/V or √(P/R) |
| Resistance | V/I | - | - | V²/P or P/I² |
| Power | V x I | V²/R | I² x R | - |
Ohm's Law Pie Chart
Electricians memorize this with a pie chart: V at the top, with I, R underneath (V=IR). Cover the unknown quantity to see the formula. The same technique works for the power triangle (P, V, I).Common Applications
- LED current limiting - to safely run a 2 V LED at 20 mA from a 12 V source, you need (12 - 2) / 0.02 = 500 ohms.
- Speaker load matching - a 4 ohm speaker at 20 V drives P = V2/R = 400/4 = 100 W.
- Shunt resistor sizing - to measure 10 A by dropping 50 mV, R = V/I = 0.05/10 = 0.005 ohms.
- Heating element design - a 1500 W heater on 120 V draws I = P/V = 12.5 A through a resistance of V2/P = 9.6 ohms.
AC Caveats
Ohm's Law in its pure form applies to DC and resistive AC loads. For reactive AC circuits (motors, transformers, capacitors), replace R with impedance Z, and remember that real power requires the power factor: P = V*I*PF. The basic V=IR still holds instantaneously but not for RMS calculations on reactive loads.