Series circuits

Two 12 Ω bulbs in series on a 6 V battery each get 3 V and 0.25 A, and each glows with a quarter of the power one bulb alone would have.

One path for the current

In a series circuit the parts are joined end to end, so there is only one path around the loop. Every coulomb that leaves the battery has to pass through every part in turn. That gives the first rule of series circuits: the current is the same everywhere in the loop. Put an ammeter before the first bulb, between the bulbs or after the last one and it reads the same number. Charge cannot pile up anywhere, so whatever flows into a part must flow out of it.

Resistances add

Each part takes some of the battery's voltage. Going around the loop, the voltage drops across the parts must add up to the battery's voltage, because each coulomb gives up all the energy it received. With the same current I through each part, the drops are I R₁, I R₂ and so on, and their sum is I (R₁ + R₂ + ...). So the whole chain acts like one resistor of R = R₁ + R₂ + R₃ + ... . This is why adding parts in series always increases the total resistance and lowers the current.

Working it out

Take the lab's starting circuit: a 6 V battery and two 12 Ω bulbs in series. The total resistance is 12 + 12 = 24 Ω, so the current is 6 ÷ 24 = 0.25 A. Each bulb has V = 0.25 × 12 = 3 V across it, and the two drops add to 6 V as they must. A bulb alone on the same battery would carry 0.5 A and get the full 6 V. OpenStax works a mixed example: 1.00 Ω, 6.00 Ω and 13.0 Ω in series on 12.0 V. The total is 20.0 Ω and the current 0.600 A; the drops are 0.600 V, 3.60 V and 7.80 V, which add to 12.0 V. Notice that the biggest resistor takes the biggest share of the voltage.

What series is good for, and what it is bad at

Because there is one path, a single switch anywhere in the loop controls everything. That is exactly how a light switch works: it sits in series with the lamp it controls. Fuses and circuit breakers are also put in series, so that all the current must pass through them. The same property is the weakness of series wiring. If one bulb burns out, its filament breaks, the loop is open, and every other bulb in the chain goes dark too. Try it in the lab by removing one bulb.

Adding bulbs in series also makes them dimmer. With three 12 Ω bulbs on 6 V the total is 36 Ω and the current 6 ÷ 36 ≈ 0.167 A, so each bulb gets only 2 V. The battery's voltage is shared out among more and more parts, and each gets a smaller slice. Batteries themselves can be put in series to add their voltages: two 1.5 V cells end to end give 3 V, and four give 6 V. Put one in the wrong way round and its voltage subtracts instead.