Why do we sometimes use P = I²R instead of P = E × I?
GeneralClass 12AllAnswered 27 Mar 2026
Answer
Both formulas are valid—they serve different analytical purposes:
P = E × I (or P = V × I):
- Shows total power in the circuit
- Easy when voltage and current are known
- Best for calculating consumed power
- Used for overall circuit analysis
P = I²R:
- Shows power dissipated as heat in a resistor
- Highlights how current affects power loss
- Critical for analyzing power loss in wires
- Used for thermal management
Insight: P = I²R emphasizes that power loss increases with the square of current, which is why high-voltage transmission lines use lower current to reduce losses.
Example: In a 10Ω wire carrying 5A at 50V:
- Total power: P = 50 × 5 = 250W
- Power loss in wire: P = 5² × 10 = 250W
- (All power is lost to heat in this case!)
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