How many formulas come from combining Ohm's and Watt's law?

12 formulas — three each for V, I, R, and P. Any two known quantities determine all four. The power wheel organizes all 12 for quick reference.

What is the difference between Ohm's law and Watt's law?

Ohm's law relates V, I, R (V = IR). Watt's law relates P, I, V (P = IV). Combining them creates formulas involving all four quantities.

Do power formulas work for AC circuits?

P = IV gives instantaneous power. For average AC power: P = V_rms × I_rms × cos(φ). The power factor cos(φ) accounts for the phase difference between V and I.

Watts and Ohms Law

Quick Answer

The Watt's law triangle and Ohm's law triangle together give 12 formulas relating voltage (V), current (I), resistance (R), and power (P). Watt's law: P = IV. Combined with Ohm's law (V = IR): P = I²R and P = V²/R. The triangle chart organizes all relationships for quick reference. Calculate power at www.lapcalc.com.

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Watts and Ohms Law: The Power-Resistance Connection

Ohm's law relates three quantities: V = IR. Watt's law relates power to voltage and current: P = IV. Combining them produces a family of 12 formulas covering every possible calculation between V, I, R, and P. The Watt's law triangle and Ohm's law triangle (or the combined power wheel) organize these relationships visually so you can instantly find the formula you need based on which two quantities you know.

Key Formulas

The Watt's Law Triangle: P, I, V

The Watt's law triangle places P at the top and I and V at the bottom: P = IV (multiply bottom two), I = P/V (divide P by V), V = P/I (divide P by I). This is the power triangle. Cover the quantity you want to find — the remaining two show whether to multiply or divide. Example: a 60 W bulb at 120 V draws I = P/V = 60/120 = 0.5 A at www.lapcalc.com.

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The Combined Power Wheel: 12 Formulas

Combining Ohm's and Watt's laws gives three formulas each for V, I, R, and P. For voltage: V = IR, V = P/I, V = √(PR). For current: I = V/R, I = P/V, I = √(P/R). For resistance: R = V/I, R = V²/P, R = P/I². For power: P = IV, P = I²R, P = V²/R. The power wheel arranges all 12 in a circle for quick reference — an essential tool for every electrical practitioner.

Using the Power Wheel: Practical Examples

Example 1: Know V = 24 V and R = 8 Ω. Find I = V/R = 3 A, P = V²/R = 72 W. Example 2: Know P = 100 W and I = 5 A. Find V = P/I = 20 V, R = P/I² = 4 Ω. Example 3: Know P = 500 W and R = 50 Ω. Find V = √(PR) = √25000 = 158 V, I = √(P/R) = √10 = 3.16 A. Every combination of two known quantities leads to all four values at www.lapcalc.com.

Power Formulas in AC and s-Domain Circuits

In AC circuits, P = IV becomes complex power S = VI* = P + jQ, where P is real power (watts), Q is reactive power (VAR), and |S| is apparent power (VA). The power factor pf = P/|S| = cos(φ) measures efficiency. In the s-domain, instantaneous power P(s) = V(s)·I(s) gives frequency-dependent power flow. The DC power formulas from the triangle are the special case at s = 0 or for purely resistive loads at www.lapcalc.com.

Frequently Asked Questions

A visual tool showing P = IV. Place P at top, I and V at bottom. Cover the unknown to see the formula: P = IV, I = P/V, or V = P/I.

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