What if you added more bulbs in a row?

Olly has one bulb and a battery. The bulb glows brightly.

Now he wants more light. What if he adds more bulbs to the same loop, one after another?

A single bulb joined to a battery in a loop of wire glows nicely. If you want more light, adding more bulbs seems like a good idea. But how you add them matters.

In this lab, Olly adds bulbs in a row, called series: the current has only one path, so it must pass through every bulb in turn. Will each bulb glow just as brightly as the first one did? Brighter? Or dimmer?

A series connection puts components one after another on a single path, so the same current must pass through each. This lab starts with one 3 Ω bulb on an ideal 3 V battery and adds identical bulbs in series, up to four.

The question is quantitative: how do the current, the voltage across each bulb and each bulb's power change as the number of bulbs n rises from one to four?

With one bulb, all the battery's push goes to that bulb.

Lots of electricity flows. The bulb glows brightly.

With only one bulb in the loop, the bulb gets the battery's whole push: all 3 volts. One amp of current flows, and the bulb turns 3 watts of power into light and heat.

The model calls this 100 percent brightness, or full glow. It is the yardstick for the rest of the lab: every other brightness in this lab is compared with these 3 watts.

With n = 1, the loop resistance is 3 Ω, so I = 3 V ÷ 3 Ω = 1.00 A. The bulb has the full 3.00 V across it and dissipates P = IV = 3 W. Over the model's 12-second run, that is 36 J.

The model's brightness readout is P divided by a fixed 3 W full glow, exactly this single bulb's power, so it reads 100%. The readout compares electrical power, not measured light.

Olly adds a second bulb in the row. Both glow, but dimmer.

He adds a third and a fourth. Now all four bulbs are very dim!

Add a second bulb in the row and the current halves to 0.50 amps; each bulb gets 1.5 volts and glows at 25 percent. With three bulbs, each gets 1 volt and glows at 11 percent. With four, the current is only 0.25 amps, each bulb gets 0.75 volts, and each glows at just 6 percent.

Surprise: four bulbs together use less power than one bulb did on its own, only 0.75 watts instead of 3. Adding bulbs in a row makes less light overall, not more.

Each added bulb raises the loop resistance by 3 Ω: 6, 9 and 12 Ω for n = 2, 3 and 4. The current falls as 1/n, to 0.50, 0.33 and 0.25 A, and the voltage across each bulb falls to 1.50, 1.00 and 0.75 V.

Power per bulb falls as 1/n²: 0.75, 0.333 and 0.187 W, which the readout shows as 25%, 11% and 6%. Total power falls as 1/n too, from 3 W to 0.75 W, so the 12-second run uses 9 J instead of 36. Now take bulb 1 out: with one path, every bulb goes dark.

Each bulb makes it harder for electricity to flow.

More bulbs in a row means less electricity flows. The bulbs also share the battery's push. So each one glows dimmer.

Every bulb resists the flow of current. In a row, the current has to get through all of them, so their resistances add up. Four bulbs resist four times as much as one, so only a quarter of the current flows.

The bulbs also share the battery's push: four bulbs get a quarter each. A quarter of the push and a quarter of the current gives each bulb a sixteenth of the power. Our model keeps each bulb's resistance fixed, its battery never runs down, and it compares brightness by power.

OpenStax shows why: in series, all the current must pass through each resistor, so R_s = R₁ + R₂ + …, and the voltage drops across the resistors add up to the source voltage. For n identical bulbs, I = V/(nR) and each bulb drops V/n, so P = V²/(n²R).

Model limits: the bulbs are ohmic, but a real tungsten filament's resistance rises steeply as it heats (OpenStax works an example from 0.350 Ω cold to 4.8 Ω at 2,850 °C). A metal's resistivity rises with temperature, so a dim, cooler filament should have less resistance than the same filament glowing hot, and real series bulbs will not follow these exact numbers. The battery is ideal, wires have no resistance and brightness means power, not light output.

Some strings of holiday lights have many tiny bulbs in one long row.

Each tiny bulb is made for a small push. Together they share a big push.

Some strings of holiday lights are wired in series. A US patent for light strings describes a typical string of 50 lights in a row plugged into 120 volts, with each bulb made for about 2.5 volts, its small share of the push.

The same patent says that adding more bulbs to such a string brings the brightness down, just like in Olly's lab. Because all the bulbs share one path, these strings need special parts so one broken bulb doesn't switch off the whole string.

Series wiring suits many small, identical loads that share a high source voltage. US Patent 7,279,809 B2 describes a typical 50-light series string operated at 120 volts AC with bulbs designed for about 2.5 volts, and notes that adding more bulbs to a string that runs too bright, or using lower-current or higher-voltage-rated bulbs, brings the brightness down.

The weakness is the single path: one open filament breaks the whole circuit, which is why such strings use shunts across each bulb (see the lab on a broken bulb). Household outlets and lights, by contrast, are wired in parallel, so each device gets the full voltage.