The Memory Trick
💡 Three Forms, One Formula
Electrical power can be calculated three different, mathematically equivalent ways: P = IV (current times voltage), P = I²R (current squared times resistance), or P = V²/R (voltage squared divided by resistance). All three come directly from combining P = IV with Ohm's Law (V = IR) — pick whichever form matches the variables a given problem provides.
Why It Works
Since V = IR (Ohm's Law), you can substitute for either V or I in the base formula P = IV to eliminate whichever variable you don't have — substituting V = IR gives P = I²R, while substituting I = V/R gives P = V²/R. They're not three separate rules to memorize independently, just one relationship viewed three ways.
Step by Step
Choosing the Right Form
1
Use P = IV when you know current and voltage
This is the most direct, fundamental form — power equals current times voltage.
A device drawing 2 A at 120 V consumes P = 2 × 120 = 240 W.
2
Use P = I²R when you know current and resistance
Useful specifically when voltage isn't given directly but current and resistance are.
A 5 A current through a 10 Ω resistor dissipates P = 5² × 10 = 250 W.
3
Use P = V²/R when you know voltage and resistance
Useful specifically when current isn't given directly but voltage and resistance are.
A 120 V supply across a 60 Ω resistor dissipates P = 120²/60 = 14,400/60 = 240 W.
🏥 Worked Example
A 100 W light bulb is designed to operate at 120 V. What current does it draw, and what is its resistance?
1
Find current using P = IV: I = P/V = 100/120 ≈ 0.833 A.
2
Find resistance using P = V²/R: R = V²/P = 120²/100 = 14,400/100 = 144 Ω.
3
Verify with a third form: P = I²R = (0.833)² × 144 ≈ 0.694 × 144 ≈ 100 W — confirms consistency across all three formulas.
📌 Exam Application
Exams test the ability to select the correct power formula based on which variables are given, and to correctly derive one unknown quantity by combining P = IV with Ohm's Law when necessary.
⚠️ Most Common Electrical Power Mistakes
The most common trap is trying to memorize all three power formulas as independent, unrelated facts — recognizing they're all derived from the same P = IV combined with Ohm's Law (V=IR) makes it far easier to derive whichever form you need on the spot, rather than needing to recall all three from memory.
✓ Quick Self-Test
1) Write the three equivalent formulas for electrical power. P = IV, P = I²R, P = V²/R. 2) What law connects these three formulas together? Ohm's Law (V = IR), by substitution into P = IV. 3) Which power formula would you use if you know current and resistance, but not voltage? P = I²R. 4) Which power formula would you use if you know voltage and resistance, but not current? P = V²/R. 5) What are the units of electrical power, and what do they mean physically? Watts (W), equivalent to Joules per second — the rate of energy transfer.
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