Heating effect of current
The heat produced in a resistor is H = I²Rt, Joule's law of heating. A 4 Ω resistor carrying 2 A for 5 s gives H = 2² × 4 × 5 = 80 J.
Ohm's law
V = IR at a fixed temperature. Pick what to find and type the other two. Add a time to get the heat, H = I²Rt, and the energy in kWh.
Voltage V8 V
Power16 W
Heat80 J
Energy2.22 × 10⁻⁵ kWh
- V = IR = 2 × 4 = 8 V
- Power: P = VI = 8 × 2 = 16 W. The same as I²R and V²/R.
- Heat in 5 s: H = I²Rt = 2² × 4 × 5 = 80 J
- In units of electrical energy: 80 J / (3.6 × 10⁶ J per kWh) = 2.22 × 10⁻⁵ kWh
Why it works
- A charge Q moving through a potential difference V has work W = VQ done on it.
- In a time t a steady current I carries Q = It, so W = VIt.
- In a resistor all of this energy becomes heat: H = VIt.
- With V = IR this is H = I²Rt. The heat goes as the square of the current, and with the resistance and the time.
- It is put to use in the electric iron, toaster, heater, bulb filament and fuse.
Heating effect of current: quick answers
What is Joule's law of heating?
The heat produced in a resistor is proportional to the square of the current, to the resistance and to the time: H = I²Rt.
How does a fuse protect a circuit?
A fuse is a short wire with a low melting point in series with the circuit. Too large a current heats it until it melts and breaks the circuit.
Why is tungsten used for bulb filaments?
It has a very high melting point, about 3380 °C, so it can glow white hot without melting. The bulb is filled with an inert gas so it does not burn.