Finding current and resistance for an immersion heater using V, I, R and power relationships.
This worked example treats an immersion element as a simple resistive load, and uses Ohm’s law with the power formula to keep current (amps) and resistance (ohms) apart. The same shortcuts do not work for every AC motor or pump.
The relationships. For this resistive element, V = I × R and P = V × I, using RMS voltage and current on AC. Therefore I = P / V and R = V / I = V² / P.
The situation. A 3 kW (3000 W) immersion heater runs from a 230 V supply.
Step 1 — find the current. I = P / V = 3000 / 230 = about 13.0 amps (A).
Step 2 — find the resistance. R = V / I = 230 / 13.04 = about 17.6 ohms. The same figure comes straight from the power rating, R = V² / P = 52,900 / 3000 = 17.6 ohms, which avoids rounding the current first.
Why it matters. The element draws about 13 A, but its resistance is about 17.6 Ω: these answer different questions. Load current helps select the circuit; cable installation conditions, protective-device requirements and the appliance instructions also matter.
Takeaway. The resistance worked out here is for this element, at its stated operating condition. Electrical work needs the right competence and checking under the rules that apply. In England, Approved Document P gives guidance for electrical safety in dwellings. Securely isolate and prove dead before work.
Common calculation traps
Keep units consistent. In this working, enter power in watts, voltage in volts, current in amps and resistance in ohms. Convert prefixes before substituting: using 3 instead of 3,000 W changes the result by a factor of 1,000. Use the voltage specified for the exercise or the actual equipment data for the task, and keep sufficient precision until the final answer.
The 17.6 Ω result describes the hot heater element, not its supply cable. It is also not a way to find an AC motor winding’s resistance from the motor’s rated watts and supply voltage. AC motors involve impedance, power factor and conversion to mechanical output. Use the manufacturer’s electrical data and specified tests for a motor or pump.
Finally, the calculated current is only what this load should draw when it is on. It tells you nothing about whether its conductors are safe to work on. A second supply, a borrowed neutral or stored charge may still present a hazard. Identify the relevant sources, secure their isolation, control stored energy and test for absence of voltage at the work point using a suitable detector checked before and after. Load calculations help plan the circuit; they cannot tell you whether it is live or dead.
Series and parallel loads
In series, resistances add and the same current flows through each: 30 Ω and 50 Ω in series make 80 Ω, so on 230 V the current is 230 ÷ 80, about 2.9 A. In parallel, each path has the full supply voltage across it, and the combined resistance is less than the smallest one: 1/R = 1/R1 + 1/R2. Two equal 40 Ω elements in parallel make 20 Ω.
Power, current and voltage
Power is voltage times current, P = V × I, so current is power divided by voltage. An 8.5 kW electric shower on 230 V draws 8500 ÷ 230, about 37 A, which is why a shower needs its own suitably rated circuit, designed and installed by a competent person. For a resistive element P = V² ÷ R, so its power falls with the square of the voltage: Heatrae Sadia rates one immersion heater at 3.0 kW on 240 V and 2.8 kW on 230 V.
Energy is power multiplied by time. With power in kilowatts and time in hours, energy = power × time gives kilowatt-hours (kWh), the unit on an electricity bill. Convert minutes to hours first by dividing by 60: a 3 kW immersion heater running for 90 minutes runs for 1.5 h and uses 3 × 1.5 = 4.5 kWh.
Cable size and heating
A conductor's resistance rises with its length and falls as its cross-sectional area grows: R = ρL ÷ A. The heat produced in it is P = I²R, so doubling the current through the same cable makes four times the heat. That is why a circuit carrying tens of amps, such as an electric shower's, uses much thicker cable than a lighting circuit carrying a few amps; the actual size follows the protective device, the way the cable is installed and BS 7671.
The supply cables into a house have resistance too, so a large current drops voltage along them (V = I × R). That is why the lights can dim when a big load such as an electric shower is switched on: less voltage is left for everything else.
Alternating and direct current
Direct current (DC) flows one way, as from a battery. Alternating current (AC) reverses direction again and again: the mains in Great Britain is declared at 230 V and 50 hertz, which means 50 complete cycles every second. Unless agreed otherwise, the frequency may vary by no more than 1% either way, and the voltage by up to 10% above or 6% below 230 V, from 216.2 V to 253 V.
A transformer steps an AC voltage up or down. Its two coils are wound on an iron core and are not joined: the changing current in the primary coil makes a changing magnetic field, and that induces a voltage in the secondary. A steady direct current makes a steady field, which induces nothing, so a transformer cannot change a DC voltage. Almost all the power goes through, so when the voltage is stepped down the current goes up in the same ratio: a 230 V to 110 V site transformer gives about twice as much current on its 110 V side as it takes from the 230 V supply.