---
title: "Series and Parallel Circuits"
book: "Primary & Middle School Physics"
subject: physics
language: en
chapter: 30
exercises: 11
source: https://one-course.com/books/physics/1/en/chapter/30-series-and-parallel-circuits
---

# Chapter 30 — Series and Parallel Circuits

When one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) died, the whole party string went dark — the curse of the single loop. Yet when a [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) burns out in your kitchen, the rest of the house shines on. Somebody wired your house a cleverer way. Today we learn it: the way of the [branches](#def-g5-series-parallel-circuits-parallel).

## 30.1 Two ways to wire

You know the first way: *[in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series)*, all players threaded on one loop, beads on one necklace. Here is the second.

**Definition 30.1 (In parallel).**

Players are *in parallel* when the circuit splits into separate *branches* — one player per branch — that fork apart and rejoin. The points where roads fork or rejoin are called *junctions*. Each branch is a complete road from one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) [terminal](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) to the other.

![Two bulbs in parallel: the road forks at one junction, each bulb rides its own branch, and the branches rejoin before returning to the battery.](https://one-course.com/images/onecourse/chapters/physics-1/g5-series-parallel-circuits/fig-c577fadbf6d6.svg)

*Two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [in parallel](#def-g5-series-parallel-circuits-parallel): the road forks at one [junction](#def-g5-series-parallel-circuits-parallel), each [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) rides its own [branch](#def-g5-series-parallel-circuits-parallel), and the [branches](#def-g5-series-parallel-circuits-parallel) rejoin before returning to the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery).*

**Method 30.2 (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) and wires:

1. wire 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 [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) , alone, as a plain loop — [branch](#def-g5-series-parallel-circuits-parallel) one;
2. now wire the second [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) *directly across* the first: one wire from each side of [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 to the matching side of [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 — [branch](#def-g5-series-parallel-circuits-parallel) two;
3. trace each [branch](#def-g5-series-parallel-circuits-parallel) with your finger: from $+$ , every road should pass exactly one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) before reaching $-$ .

Both [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) — and both shine as brightly as a single [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) would alone.

## 30.2 The rules of the branches

**Proposition 30.3 (Rules of the parallel circuit).**

With each player on its own [branch](#def-g5-series-parallel-circuits-parallel):

1. *independence* : a gap in one [branch](#def-g5-series-parallel-circuits-parallel) stops only that [branch](#def-g5-series-parallel-circuits-parallel) — unscrew one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) , and the other burns on;
2. *full brightness* : each [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) shines as if it were alone — no sharing of the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ’s push between [branches](#def-g5-series-parallel-circuits-parallel) ;
3. *command posts* : a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) inside a [branch](#def-g5-series-parallel-circuits-parallel) commands only that [branch](#def-g5-series-parallel-circuits-parallel) ; a switch on the common road, before the fork, commands everyone. (The price: the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) feeds every [branch](#def-g5-series-parallel-circuits-parallel) at once, and so it drains faster.)

**Example 30.4 (The unscrewing test, replayed).**

Do to the parallel pair exactly what once killed the series pair: unscrew [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2. [Bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 does not even flicker — its own [branch](#def-g5-series-parallel-circuits-parallel), its own complete road, is untouched. Screw it back, unscrew [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 instead: [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 burns calmly on. The curse of the single loop is lifted: [in parallel](#def-g5-series-parallel-circuits-parallel), every player minds its own [branch](#def-g5-series-parallel-circuits-parallel).

![Command posts: the main switch, before the fork, rules both branches; the branch switch rules only its own bulb — here it stands open, so bulb 1 shines alone.](https://one-course.com/images/onecourse/chapters/physics-1/g5-series-parallel-circuits/fig-17239d607488.svg)

*Command posts: the main [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), before the fork, rules both [branches](#def-g5-series-parallel-circuits-parallel); the [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) rules only its own [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) — here it stands open, so [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 shines alone.*

**Example 30.5 (Your house is a parallel circuit).**

Every lamp, socket and appliance in your home rides its own [branch](#def-g5-series-parallel-circuits-parallel) of one great [parallel circuit](#def-g5-series-parallel-circuits-parallel). That is why the kitchen [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) can burn out while the living room reads on undisturbed; why each room’s [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) commands only its own [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source); and why one main [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) — in the fuse box by the meter — can cut the whole house at once for repairs. Modern party [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) joined the club: their [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) are wired so one dead [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) no longer darkens the string.

**Remark 30.6 (Series and parallel, side by side).**

One gap: series — all dark; parallel — one [branch](#def-g5-series-parallel-circuits-parallel) dark. More [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): series — all dimmer; parallel — all at full brightness, but the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) drains faster. One [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) for everything: series — anywhere; parallel — only before the fork. Neither way is “better”: the flashlight is happily series (one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), one [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch)), the house is necessarily parallel. An electrician’s first question about any circuit is simply: *where does the road fork?*

## 30.3 Reading circuits

**Method 30.7 (Following the roads).**

To predict any [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb)’s fate in a circuit drawing:

1. put your finger on the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) ’s $+$ and walk every possible road to $-$ , listing the players each road passes;
2. a [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) if at least one unbroken road passes through it;
3. players sharing every road are [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) with each other; players on different forks are [in parallel](#def-g5-series-parallel-circuits-parallel) .

Walk the roads before you predict — guessing from the drawing’s shape alone is how circuits fool people.

## 30.4 Exercises

**Exercise 30.1 ★.**

What is a [branch](#def-g5-series-parallel-circuits-parallel)? A [junction](#def-g5-series-parallel-circuits-parallel)? In a [parallel circuit](#def-g5-series-parallel-circuits-parallel) with two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), how many [branches](#def-g5-series-parallel-circuits-parallel) carry a [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb)?

**Solution of Exercise 30.1.**

A [branch](#def-g5-series-parallel-circuits-parallel) is one of the separate roads the circuit forks into; a [junction](#def-g5-series-parallel-circuits-parallel) is a point where roads fork or rejoin. Two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [in parallel](#def-g5-series-parallel-circuits-parallel) ride two bulb-carrying [branches](#def-g5-series-parallel-circuits-parallel).

**Exercise 30.2 ★.**

State the three rules of the [parallel circuit](#def-g5-series-parallel-circuits-parallel).

**Solution of Exercise 30.2.**

Independence (a gap stops only its own [branch](#def-g5-series-parallel-circuits-parallel)); full brightness (each [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) shines as if alone, the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) draining faster in return); command posts (a [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) rules its [branch](#def-g5-series-parallel-circuits-parallel), a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) before the fork rules all).

**Exercise 30.3 ★.**

Two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) [in parallel](#def-g5-series-parallel-circuits-parallel): [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 is unscrewed. What does [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 do? And in the series pair — what did it do there, and why the difference?

**Solution of Exercise 30.3.**

[Bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 burns on, undisturbed — its own road is complete. [In series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) it went dark, because there the two [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) shared one single road, and any gap broke it for both.

**Exercise 30.4 ★.**

Two identical [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb): pair A is [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series), pair B [in parallel](#def-g5-series-parallel-circuits-parallel), same batteries. Which pair shines brighter per [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb)? Which drains its [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) faster?

**Solution of Exercise 30.4.**

Pair B (parallel) shines brighter per [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) — each at full brightness. Pair B also drains its [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) faster: it feeds two full [branches](#def-g5-series-parallel-circuits-parallel) at once.

**Exercise 30.5 ★.**

In the figure with the two [switches](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), what does each [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) do when: both [switches](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) closed? main open? main closed, [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) open?

**Solution of Exercise 30.5.**

Both closed: both [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) shine. Main open: both dark — it rules the common road. Main closed, [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) open: [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 1 shines, [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 dark.

**Exercise 30.6 ★.**

Why is a house wired [in parallel](#def-g5-series-parallel-circuits-parallel) and not [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series)? Give two everyday comforts that depend on it.

**Solution of Exercise 30.6.**

[In series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series), one dead [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) (or one switched-off lamp!) would darken the whole house, and everything would dim as more [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) joined. Comforts from parallel wiring: each room’s [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) rules only its room; a burnt-out kitchen [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) leaves the rest of the house lit; every lamp burns at full brightness.

**Exercise 30.7 ★.**

Where in a house circuit does a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) command everything at once? What is that [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch)’s everyday name and use?

**Solution of Exercise 30.7.**

Before the fork — on the common road where the current enters the home: the main [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) in the fuse box. It cuts the whole house at once, used for repairs and emergencies.

**Exercise 30.8 ★.**

A bedside lamp and its wall socket: are they [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) or [in parallel](#def-g5-series-parallel-circuits-parallel) with the ceiling [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source)? How do you know from daily life?

**Solution of Exercise 30.8.**

[In parallel](#def-g5-series-parallel-circuits-parallel): switching the ceiling [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) off does not kill the bedside lamp, and unplugging the lamp does not darken the ceiling — each rides its own [branch](#def-g5-series-parallel-circuits-parallel).

**Exercise 30.9 ★★.**

Draw (with symbols) a circuit for a hallway: one [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb), and this comfort — the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) must go on and off from a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) at *either* end of the hallway… Try honestly; if your designs stubbornly fail, explain what is hard. (True two-way switching needs a cleverer [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) than ours — the attempt teaches more than the answer.)

**Solution of Exercise 30.9.**

With our plain [switches](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) the designs keep failing: a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) with the [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) can be opened from one end only; two plain [switches](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) demand *both* closed (either end can turn the [light](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) off but not always on); two [in parallel](#def-g5-series-parallel-circuits-parallel) demand both open for darkness. The hallway comfort needs a [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) that *chooses between two roads* instead of just breaking one — the two-way [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch), which real hallways use in matched pairs.

**Exercise 30.10 ★★.**

A string of modern party [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) keeps shining when one [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) dies — but the box warns: “Do not run the string with more than three [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) removed.” Using the rules of the [branches](#def-g5-series-parallel-circuits-parallel), explain both the comfort and, harder, a sensible reason for the warning. (Think of what each remaining [branch](#def-g5-series-parallel-circuits-parallel) receives from the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery), and of the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery)’s own effort.)

**Solution of Exercise 30.10.**

The comfort: the [bulbs](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) ride parallel [branches](#def-g5-series-parallel-circuits-parallel), so a dead [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) darkens only itself. The warning: every missing [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) removes a [branch](#def-g5-series-parallel-circuits-parallel), and the [battery](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-battery) (or the string’s little power supply) pushes its full effort through the [branches](#def-g5-series-parallel-circuits-parallel) that remain — with too many gone, the survivors each receive more than they were built for, burn hotter, and fail young.

**Exercise 30.11 ★★.**

In the [two-switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) figure, an electrician wants to add one more [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) that [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) *only* when the [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) is closed, and is dark otherwise — even with the main [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) closed. Onto which stretch of road must the new [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) be wired, and is it then [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) or [in parallel](#def-g5-series-parallel-circuits-parallel) with [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2?

**Solution of Exercise 30.11.**

Onto the [branch-switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch)’s own stretch of road: between the [branch](#def-g5-series-parallel-circuits-parallel) [switch](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#ex-g3-first-electric-circuit-switch) and [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2 (before their [branch](#def-g5-series-parallel-circuits-parallel) rejoins the rest). There it [lights](https://one-course.com/books/physics/1/en/chapter/3-light-and-shadows#def-g1-light-and-shadows-source) exactly when that [branch](#def-g5-series-parallel-circuits-parallel) runs — and it sits [in series](https://one-course.com/books/physics/1/en/chapter/23-series-circuits#def-g4-series-circuits-series) with [bulb](https://one-course.com/books/physics/1/en/chapter/16-a-first-electric-circuit#def-g3-first-electric-circuit-bulb) 2, both riding the same [branch](#def-g5-series-parallel-circuits-parallel).