Ohm's Law, Power, LED Resistors, and Series and Parallel Resistors
October 29, 2026
Ohm's law links voltage (V), current (I), and resistance (R): V = I × R. Power is P = V × I = I² × R = V² ÷ R. A 12 V supply across a 4-ohm load drives I = 12 ÷ 4 = 3 amps, and the power is 12 × 3 = 36 watts.
If the current rises, heat in the resistor increases with its square: a resistor carrying 3 A with 4 ohms dissipates 3² × 4 = 36 W, which requires a heavy-duty resistor, since small ones are rated at ¼ or ½ watt.
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In series, resistances add: R = R₁ + R₂ + R₃. For 100, 220, and 330 ohms: 650 ohms. In parallel, reciprocals add: 1/R = 1/R₁ + 1/R₂. For 100 and 220 ohms in parallel: 1/R = 0.01 + 0.004545 = 0.014545, so R = 68.75 ohms, smaller than either one. Two equal resistors in parallel give half the value. For two resistors, R = (R₁ × R₂) ÷ (R₁ + R₂) = 22,000 ÷ 320 = 68.75. Parallel paths provide more routes for current, so the total resistance falls.
| Circuit | Calculation | Result |
|---|---|---|
| 12 V across 4 ohms | I = 12 / 4 | 3 A, 36 W |
| 100 + 220 + 330 ohms in series | sum | 650 ohms |
| 100 and 220 ohms in parallel | 100 x 220 / 320 | 68.75 ohms |
| Two 100 ohm resistors in parallel | 100 / 2 | 50 ohms |
LED Resistor
An LED needs a resistor to limit current. R = (supply voltage − LED forward voltage) ÷ desired current. With a 5 V supply, a red LED with a 2.0 V drop, and 20 mA: R = (5 − 2.0) ÷ 0.020 = 150 ohms. The resistor dissipates P = I² × R = 0.02² × 150 = 0.06 W, so a ¼-watt resistor is plenty. Using the next standard value above (such as 180 ohms) lowers the current to 16.7 mA with slightly less brightness, and extends the LED's life. Blue and white LEDs drop 3 V or more.
Energy and Cost
Energy in kWh = power in kW × hours. A 1,500 W space heater running 3 hours uses 1.5 × 3 = 4.5 kWh, costing $0.72 at $0.16 per kWh. Current from household power: at 120 V, a 1,500 W heater draws 12.5 A, so a 15-amp circuit (1,800 W capacity, 1,440 W for continuous loads under the 80% rule) is at its limit. That is why a heater and another appliance on the same circuit can trip the breaker.
Safety
Mains voltage can be lethal; the math is the same, but work on household wiring should be done by qualified people. Use components rated for the power and voltage, and calculate power dissipation for every resistor.
Frequently Asked Questions
What is Ohm's law?
V = I × R.
How do I find power?
P = V × I, or I² × R, or V² ÷ R.
How do I combine resistors in parallel?
Add the reciprocals, or use the product over sum for two.
How do I choose an LED resistor?
(Supply voltage − LED voltage) ÷ desired current.
How much current does a 1,500 W heater draw at 120 V?
12.5 A.