Engineering
Ohm's Law, electrical power (Watts), and parallel resistance formulas
Calculate Current (V / R), Power dissipation (V^2 / R and I^2 * R), and Series vs Parallel equivalent resistance 1 / SUM(1 / R_range).
Ohm's Law, Joule power, and reciprocal parallel resistance
Ohm's Law relates Voltage V (volts), Current I (amps), and Resistance R (ohms): V = I * R, I = V / R, and R = V / I. Electrical power in Watts equals P = V * I = I^2 * R = V^2 / R.
Resistors in SERIES add directly: R_series = SUM(R1:Rn). Resistors in PARALLEL add by reciprocals (conductances): R_parallel = 1 / SUM(1 / R1:Rn) — which is strictly smaller for at least two positive finite branches than the smallest individual branch resistor!
| Circuit Calculation (V = 24V, R = [12, 6, 4] ohms) | Formula | Result |
|---|---|---|
| Series Resistance | =SUM(A2:A4) = 12 + 6 + 4 | 22.0 ohms |
| Parallel Resistance | =1 / SUM(1 / A2:A4) | 2.0 ohms (< 4 ohms!) |
| Total Current (Parallel @ 24V) | =24 / 2.0 | 12.0 Amps |
| Total Power Dissipated | =24^2 / 2.0 (= 24 * 12) | 288.0 Watts |
Parallel equivalent resistance and circuit power formulas
Reciprocal array division 1 / SUM(1 / A2:A4) works for 2, 3, or N parallel branches cleanly.
=ROUND(1 / SUM(1 / A2:A4), 4)Total power dissipated across parallel bank at Voltage B2
Computes V^2 / R_eq in Watts.
=ROUND((B2 ^ 2) / (1 / SUM(1 / A2:A4)), 2)Inputs and interpretation
These formulas describe ideal positive finite ohmic resistors at steady DC, or pure resistance with appropriate RMS AC values. General AC loads require impedance and power factor. Parallel resistance is strictly below the smallest branch only with at least two positive finite branches. The calculation does not size wiring, protection or thermal ratings; power dissipation must be checked against component ratings.
Try the example
Use the original values or change them to test your understanding.