The Basic Power Formula

Electrical power is the product of voltage and current.

The basic equation is:

P = V × I

Where:

• P = Power (Watts)
• V = Voltage (Volts)
• I = Current (Amperes)

Power Formulas Using Ohm's Law

Because voltage, current and resistance are related by Ohm's Law, several equivalent power formulas can be derived.

Deriving the Formulas

From Ohm's Law:

V = I × R

Substituting this into the basic power equation gives:

P = I²R

Likewise, replacing current with V/R gives:

P = V²/R

Example 1 – Using P = VI

A 12 V power supply delivers 3 A.

Power:

P = 12 × 3 = 36 W

Example 2 – Using P = I²R

A resistor has a resistance of 10 Ω and carries a current of 5 A.

Power:

P = 5² × 10

P = 25 × 10 = 250 W

Example 3 – Using P = V²/R

A resistor is connected across a 24 V supply and has a resistance of 12 Ω.

Power:

P = 24² ÷ 12

P = 576 ÷ 12 = 48 W

Which Formula Should You Use?

Applications

• Choosing resistor wattage.
• Designing power supplies.
• Sizing amplifier components.
• Battery power calculations.
• Calculating motor power.
• Selecting fuses and circuit breakers.
• Estimating electrical energy consumption.

Power Ratings

Always choose components with power ratings greater than the calculated power.

For example, if a resistor dissipates 0.4 W, a ½ W resistor may become quite hot. A 1 W resistor would provide a safer operating margin and longer service life.

Common Mistakes

• Using voltage instead of current in the wrong formula.
• Forgetting to square the current in P = I²R.
• Forgetting to square the voltage in P = V²/R.
• Mixing volts, millivolts, amperes and milliamperes.
• Selecting resistors with insufficient power ratings.

Quick Practice

Answers

Key Points

• The basic power formula is P = V × I.
• P = I²R is useful when current and resistance are known.
• P = V²/R is useful when voltage and resistance are known.
• Always use consistent units.
• Select components with adequate power ratings.
• Power calculations are essential for safe circuit design.