How Does Power Work When Appliances Are Connected in Series?

When appliances are connected in series, they carry one shared current, and the source voltage is divided across them. As a result, an appliance’s power in the series circuit is usually different from the power printed on its label.

The label gives a rated power: the power the appliance is designed to use when operated under its specified conditions, usually at its rated voltage. To work out what happens in series, calculate the circuit current and then the power dissipated by each appliance.

The series-circuit rule

For ideal resistive appliances, use the power-rating relationship to estimate each appliance’s resistance:

$R=\frac{V_{\text{rated}}^2}{P_{\text{rated}}}$

If the appliances are in series, their resistances add, and the same current flows through each:

$R_{\text{total}}=R_1+R_2+\cdots, \qquad I=\frac{V_{\text{supply}}}{R_{\text{total}}}$

Then calculate each appliance’s actual power using the current through it:

$P_i=I^2R_i$

This shows why the appliances do not necessarily use equal power: the current is the same, but their resistances may differ. The appliance with the greater resistance dissipates more power in this idealized series circuit.

Worked example: two rated bulbs

Suppose two resistive bulbs are each rated for 220 V. One is rated at 100 W and the other at 60 W. Connect them in series across a 220 V supply. Treat each bulb as a fixed resistor for this calculation.

First, calculate their rated resistances:

R_{100}&=\frac{(220\text{ V})^2}{100\text{ W}}=484\,\Omega,\\ R_{60}&=\frac{(220\text{ V})^2}{60\text{ W}}\approx 806.7\,\Omega. \end{aligned}$$ The total resistance and circuit current are: $$\begin{aligned} R_{\text{total}}&=484+806.7\approx1290.7\,\Omega,\\ I&=\frac{220}{1290.7}\approx0.17045\text{ A}. \end{aligned}$$ Now find the power used by each bulb in this series arrangement: $$\begin{aligned} P_{100}&=I^2R_{100}\approx(0.17045)^2(484)\approx14.1\text{ W},\\ P_{60}&=I^2R_{60}\approx(0.17045)^2(806.7)\approx23.4\text{ W}. \end{aligned}$$ Neither bulb operates at its rated power. In this simplified calculation, the 60 W bulb uses more power in series because its rated resistance is higher. Its rating does not mean it always uses less power than a 100 W bulb; it describes its power at its specified operating voltage. The voltage division gives the same result. The 100 W bulb gets about $IR_{100}=82.5$ V, and the 60 W bulb gets about $IR_{60}=137.5$ V. Those drops add to the 220 V supply. ## Why appliances are usually connected in parallel Household appliances are generally designed to connect in parallel across the supply. In parallel, each appliance receives approximately the full supply voltage, so it can operate near its rated conditions independently of the other appliances. In series, adding or switching off one appliance changes the circuit current and affects the others; if one opens the circuit, current stops everywhere in the series path. For ideal resistive loads connected in parallel at their rated voltage, each appliance can use its rated power, and the source supplies the sum of those powers. That is not what happens when the same appliances are connected in series. ## Common mistakes - **Adding the nameplate powers in series.** Rated powers can be added when the appliances operate at their rated conditions together, as in a suitable parallel connection. In series, calculate the actual current and each actual power. - **Assuming every appliance gets the full supply voltage.** In series, the individual voltage drops add up to the source voltage; they are not each equal to it. - **Using $P=V^2/R$ with the source voltage for every appliance.** That formula uses the voltage across the particular appliance, not automatically the total supply voltage. In series, $P=I^2R$ is often the simplest method. - **Treating real appliances as fixed resistors.** The example assumes constant resistance. Incandescent-filament resistance changes substantially as the filament heats, and many electronic appliances have more complex behavior. A precise prediction may require their current-voltage characteristics or a circuit model, not just their nameplate ratings. For a first estimate with resistive appliances, use their rated voltage and power to infer resistance, solve the series circuit, and calculate power from the resulting current and voltage drops.