Intermediate · 11 min
Electrical heating in resistors
Derive resistor power relationships and calculate heating energy.
Combine voltage, current, and resistance
Electrical power is P = V × I. For an ohmic resistor with resistance R, Ohm's law gives V = I × R. Combining these gives P = I² × R or P = V² ÷ R. These are equivalent for the same resistor under the same conditions. Use the voltage across the resistor and the current through it, not unrelated supply or branch values.
Worked example
A 5 Ω resistor carries a steady current of 2 A. Power = 2² × 5 = 20 W Its voltage is 10 V, and 10 × 2 also gives 20 W.
Heating energy over time
A resistor transfers electrical energy into internal energy and to its surroundings. If power stays constant, energy transferred is E = P × t. A real resistor's temperature and resistance can change, so state when you assume a constant resistance. At fixed current, increasing resistance increases power. At fixed voltage, increasing resistance decreases power. The fixed condition determines which comparison applies.
Worked example
A resistor receiving 8 W for 10 s receives 80 J. If it transfers 30 J to its surroundings during that interval, its internal energy rises by 50 J.
State what stays constant
- For two model resistors of 4 Ω and 8 Ω, calculate power when the same current of 2 A passes through each.
- Calculate their powers instead when each has 8 V across it. Explain why increasing resistance has different effects in the two comparisons.