---
title: "Series Circuits"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 23
exercises: 11
source: https://one-course.com/books/physics/1/en/chapter/23-series-circuits
---

# Chapter 23 — Series Circuits

Last year, a string of party [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) went dark because one single [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) was missing — and we promised that its arrangement had a name. Here it is: the [series circuit](#def-g4-series-circuits-series), the simplest way to put many players on one loop. It has strict house rules, and a flashlight in your drawer has been obeying them all along.

## 23.1 One loop, several players

**Definition 23.1 (In series).**

Players in a circuit are *in series* when they sit on a single loop, one after another, like beads on one necklace: the current’s road passes through the first, then the second, then the third, with no branching anywhere. A circuit built this way is a *series circuit*.

![A series circuit: battery, switch and two bulbs on one single loop — every player threaded on the same necklace.](https://one-course.com/images/onecourse/chapters/physics-1/g4-series-circuits/fig-a627bd906579.svg)

*A [series circuit](#def-g4-series-circuits-series): [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) and two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) on one single loop — every player threaded on the same necklace.*

**Method 23.2 (Building it).**

With one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) and wires:

1. start at the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ’s $+$ [terminal](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) with a wire to the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) ;
2. wire from the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) to the first [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) , from the first [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) to the second;
3. close the loop: from the second [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) back to the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ’s $-$ [terminal](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ;
4. click the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) and watch both [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) together.

Trace the loop with your finger before switching on: if your finger must ever choose between two roads, it is not a [series circuit](#def-g4-series-circuits-series).

## 23.2 The house rules

**Proposition 23.3 (Rules of the single loop).**

In a [series circuit](#def-g4-series-circuits-series):

1. *all or nothing* : one gap anywhere — an open [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) , a broken [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) , a loose wire — and every player stops at once;
2. *order does not matter* : swap the [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) , move the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) to the other side of the loop — everything behaves exactly as before;
3. *sharing* : the more [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) on the loop, the dimmer each one glows; the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ’s push is shared along the whole necklace.

**Example 23.4 (Seeing the rules).**

Build the [two-bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) circuit and test each rule. Unscrew *either* [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): both go dark — rule one (the unscrewed socket is a gap). Swap the two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), or move the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) between them: no change at all — rule two. Now rebuild with a single [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): it shines noticeably brighter alone than it did with its partner — rule three, in reverse.

**Example 23.5 (The party lights, solved).**

The old mystery is now no mystery: the party [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) are [in series](#def-g4-series-circuits-series), dozens of beads on one necklace. One missing [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) is a gap, and rule one darkens the whole string. Finding the guilty [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) by trying them one by one taught generations of families rule one the hard way — modern strings are built differently, as next year will show.

**Remark 23.6 (The switch commands everyone).**

Rule two has a handy consequence: a single [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), placed anywhere on the loop, commands every player on it. That is why one wall [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) can control a whole row of ceiling [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — and why, for the same reason, you cannot switch off just *one* [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) of a series string without killing them all.

## 23.3 More batteries on the necklace

**Example 23.7 (Nose to tail).**

Batteries can also queue up [in series](#def-g4-series-circuits-series) — but they are fussier than [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): they must stand *nose to tail*, each [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery)’s $+$ touching the next one’s $-$. Two batteries queued this way push together, and the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) shines clearly brighter than with one. Turn one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) around — nose to nose — and the two pushes fight each other: the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) gives nothing.

![Two batteries queued nose to tail push together: the same bulb glows brighter than with one battery alone.](https://one-course.com/images/onecourse/chapters/physics-1/g4-series-circuits/fig-d7999f96a47a.svg)

*Two batteries queued nose to tail push together: the same [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) glows brighter than with one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) alone.*

**Example 23.8 (Inside the flashlight).**

Open a flashlight: the batteries slide in one behind the other in a tube — a ready-made nose-to-tail queue — then the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) and the [button-switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) complete one single loop through the case. A flashlight *is* a [series circuit](#def-g4-series-circuits-series) in a pocket. And now you know why it goes dark if a single [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) is inserted backward: nose to nose, the pushes cancel.

## 23.4 Exercises

**Exercise 23.1 ★.**

What does “[in series](#def-g4-series-circuits-series)” mean? What picture from everyday life does the chapter use for it?

**Solution of Exercise 23.1.**

Players sit on one single loop, one after another, with no branching — like beads threaded on one necklace.

**Exercise 23.2 ★.**

State the three house rules of the [series circuit](#def-g4-series-circuits-series).

**Solution of Exercise 23.2.**

All or nothing (one gap stops everyone); order does not matter (swapping players changes nothing); sharing (more [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) on the loop means each glows dimmer).

**Exercise 23.3 ★.**

In the [two-bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) circuit, [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 is unscrewed. What happens to [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1, and why? Which rule is at work?

**Solution of Exercise 23.3.**

[Bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 goes dark too. The empty socket is a gap in the single loop, and rule one — all or nothing — stops every player at once.

**Exercise 23.4 ★.**

Zoe moves the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) from before [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 to after [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2. What changes in how the circuit behaves? Which rule says so?

**Solution of Exercise 23.4.**

Nothing changes: the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) still commands both [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) exactly as before. Rule two — order on the loop does not matter.

**Exercise 23.5 ★.**

One [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) nicely. Predict the brightness with: two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [in series](#def-g4-series-circuits-series); three [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [in series](#def-g4-series-circuits-series). What is being shared?

**Solution of Exercise 23.5.**

Two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): each noticeably dimmer than the single [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) was. Three: dimmer still. The [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery)’s push is being shared along the whole necklace.

**Exercise 23.6 ★.**

How must two batteries stand to push together? Draw the queue with $+$ and $-$ marked on each [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery).

**Solution of Exercise 23.6.**

Nose to tail: the $+$ of one touching the $-$ of the next, so both push the same way around the loop. Drawing: $-\,[{+}\;{-}]\,[{+}\;
{-}]\,+$ queued in one line.

**Exercise 23.7 ★.**

Trace the loop of a flashlight: name the players the current visits from the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery)’s $+$ back to its $-$.

**Solution of Exercise 23.7.**

From $+$: through the case’s metal strip to the [button-switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), through the [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) to the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), through the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb)’s glowing thread, then back along the tube — through the second [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), nose to tail — to the first [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery)’s $-$. One loop, no branching.

**Exercise 23.8 ★.**

A doorbell circuit has a [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), a button and the bell [in series](#def-g4-series-circuits-series). Where could you add a second button so that the bell rings only when *both* buttons are pressed?

**Solution of Exercise 23.8.**

Anywhere on the same loop — for instance right after the first button. [In series](#def-g4-series-circuits-series), both buttons must be closed to complete the one road, so the bell rings only when both are pressed together.

**Exercise 23.9 ★.**

A string of ten series party [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) is dark. The [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) all look fine. Describe a patient plan, using a known-good [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), to find the broken one.

**Solution of Exercise 23.9.**

Replace the first [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) with the known-good one; if the string [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source), the removed [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) was the culprit. If not, put the original back and move to the second socket, and so on down the string. At some socket the string will [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) just removed is the broken bead.

**Exercise 23.10 ★★.**

Tom’s flashlight takes two batteries and shines brightly. After changing batteries in the dark, it gives nothing — yet both new batteries are full, the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) is fine, and no wire is loose. What has Tom done, and why does the flashlight stay dark? (See [Example 23.7](#ex-g4-series-circuits-batteries).)

**Solution of Exercise 23.10.**

In the dark, Tom slid one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) in backward. Nose to nose, the two batteries’ pushes fight instead of queuing, and the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) gets nothing — a full-strength tie is still a tie. Flipping one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) restores the nose-to-tail queue and the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source).

**Exercise 23.11 ★★.**

An engineer must place one emergency [stop-switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) for a machine whose motor sits on a single loop with its [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery). She says: “Anywhere on the loop will do.” Is she right? And why would her plan fail if the machine’s circuit had branching roads? (Next year’s chapter has the name for those.)

**Solution of Exercise 23.11.**

She is right: on a single loop, a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) anywhere commands everything — order does not matter. With branching roads, the current could detour around her [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) through another branch, and the motor might keep running; branched circuits need more careful [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) placement (they are next year’s parallel circuits).