Lesson 5 of 8Principles & Applications of Electricity

Unit 4 · Lesson 5 of 8

Series and Parallel Circuits

Loads can be connected in series (one path) or in parallel (several branches). Learn the current, potential difference and resistance rules for each, use them with Ohm's law to find missing values, and explain what happens when a bulb is removed or a branch is added, including why homes are wired in parallel.

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Key things to remember

1Series: one path; $I$ is the same everywhere; $V_{T} = V_{1} + V_{2} + \dots$ ; $R_{T} = R_{1} + R_{2} + \dots$
2Parallel: separate branches; $V$ is the same across each branch; $I_{T} = I_{1} + I_{2} + \dots$
3Adding a parallel branch decreases the total resistance and increases the total current.
4Removing one load in series stops all the current; removing one branch in parallel leaves the others working.
5Homes are wired in parallel; switches, fuses and breakers are in series with what they control.

Older strings of holiday lights had a frustrating habit: when one bulb burned out, the whole string went dark, and you had to test bulbs one by one to find the bad one. Your home works differently: switching off the kitchen light does not turn off the fridge. The difference is how the loads are connected. There are two basic ways, series and parallel, and each has its own simple rules for current, potential difference and resistance.

Series circuits: one path

In a series circuit, the loads are connected one after another, so there is only one path for the charge. Every coulomb passes through every load, so the current is the same everywhere in the loop. Each load transforms part of the energy that each coulomb carries, so the source's potential difference is shared: the potential differences across the loads add up to the source voltage. The resistances also add, so adding more loads in series raises the total resistance and lowers the current, and identical bulbs get dimmer. If any one load breaks or is removed, the only path is broken and everything stops.

Series: I_{T} = I_{1} = I_{2} = I_{3} V_{T} = V_{1} + V_{2} + V_{3} R_{T} = R_{1} + R_{2} + R_{3}

T stands for total (the source). Series: same current, voltages add, resistances add.

Parallel circuits: several branches

In a parallel circuit, each load is on its own branch. The current splits at a junction (a point where wires meet) and rejoins at another. Each branch connects straight across the source, so every branch has the same potential difference as the source. The branch currents add up to the total current from the source. Each branch works on its own: if one bulb is removed, the others keep shining just as brightly. Adding a branch gives charge one more path, like opening another checkout lane at a store, so the total current increases and the total resistance decreases. The total resistance of a parallel circuit is always less than the smallest single branch resistance.

Parallel: V_{T} = V_{1} = V_{2} = V_{3} I_{T} = I_{1} + I_{2} + I_{3} R_{T} < smallest branch R

Parallel: same voltage across each branch, currents add, total resistance is smaller than any one branch.

Fig 1The same 100 Ω and 220 Ω resistors on a 9 V source, in series (left) and in parallel (right). In series the resistances add to 320 Ω, the current is the same everywhere and the voltages add to 9 V. In parallel each resistor gets the full 9 V and the currents add; the total resistance, about 68.8 Ω, is smaller than either resistor.

ASeries

One path for current
Same current through every load
Potential differences add up to the source voltage
Total resistance = sum of the resistances
Adding a load: more total resistance, less current
One load breaks: everything stops

BParallel

Two or more branches
Branch currents add up to the total current
Same potential difference across every branch
Total resistance is less than the smallest branch
Adding a branch: less total resistance, more total current
One branch breaks: the other branches keep working

Loading interactive…

Series and parallel circuit simulator. Switch between series and parallel, set the supply voltage and two or three resistors, then compare: in series the same current flows through every resistor and their voltages share the supply; in parallel each branch gets the full voltage and the branch currents add. Watch the total resistance drop when you add a third resistor in parallel.

Going further: the parallel resistance formula

You can find a parallel circuit's total resistance with Ohm's law:

R_{T} = V_{T} \div I_{T}

. There is also a formula:

\frac{1}{R _{T}} = \frac{1}{R _{1}} + \frac{1}{R _{2}}

. For 6

Ω

and 3

Ω

in parallel,

\frac{1}{6} + \frac{1}{3} = \frac{1}{2}

, so

R_{T} = 2 Ω

, smaller than either branch. You do not need this formula for most questions in this course, but it is a good check.

Series and parallel at home

Fig 2A home's service panel feeds several branch circuits in parallel: a 15 A lighting circuit and a 20 A kitchen circuit at 120 V, and a 30 A dryer circuit at 240 V. Each branch has its own breaker and three wires: a live wire, a neutral wire that returns the current, and a ground wire that carries current only during a fault.

Homes are wired in parallel so that every outlet and light gets the full supply voltage (120 V for most outlets in Canada) and each device can be switched on and off by itself. A switch or a breaker, on the other hand, is placed in series with whatever it controls, so opening it breaks that path. Because every device you plug into a branch adds another parallel path, plugging in more devices increases the current in that branch's wires. If the current goes above the breaker's rating (for example 15 A), the breaker trips. This is called an overload, and it is why running a kettle, toaster and microwave on one kitchen circuit can cut the power.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1

A 12 V battery is connected in series with a 2.0

Ω

resistor and a 4.0

Ω

resistor. Find the total resistance, the current and the potential difference across each resistor.

Example 2

A 12 V battery is connected to a 6.0

Ω

resistor and a 3.0

Ω

resistor in parallel. Find each branch current, the total current and the total resistance.

Example 3

Three bulbs are in series with a 9.0 V battery. The voltmeter reads 4.5 V across bulb 1 and 3.0 V across bulb 2, and an ammeter beside the battery reads 0.30 A. Find the potential difference across bulb 3 and the current through it.

Example 4

Two identical bulbs are lit by a battery. Predict what happens when you unscrew one bulb if the bulbs are (a) in series, (b) in parallel.

Where marks get lost

Thinking that adding another branch in parallel increases the total resistance. Each new branch is another path, so the total resistance goes down and the total current goes up.
Believing the first bulb in a series circuit "uses up" current so later bulbs are dimmer. The current is the same through every part of a series circuit; identical bulbs in series are equally bright.
Splitting the voltage between parallel branches. Each parallel branch gets the full source voltage; it is the current that splits.
Giving every load in a series circuit the full battery voltage. In series, the potential differences add up to the source voltage.
Adding resistances in parallel as if they were in series. Parallel total resistance is always smaller than the smallest branch; if your answer is bigger, something went wrong.

Flashcards 8

Series circuit

Parallel circuit

Junction

Series rules

+ 4 more

Practice

Three identical bulbs are connected in series to a battery. One bulb burns out. What happens to the other two?

Three identical bulbs are connected in parallel to a battery. One bulb burns out. What happens to the other two?

Three resistors are in series with a 9.0 V battery. The potential differences across the first two are 2.5 V and 4.0 V. What is the potential difference across the third, in volts?

A parallel circuit has three branches carrying 0.50 A, 0.75 A and 0.25 A. What is the total current from the source, in amperes?

A source supplies a total current of 2.4 A to a parallel circuit with three branches. Two branches carry 1.0 A and 0.6 A. What is the current in the third branch, in amperes?

Resistors of 10

Ω

, 15

Ω

and 25

Ω

are connected in series to a 10 V battery. What current flows, in amperes?

A lamp is connected to a battery. A second lamp is added in parallel with it. What happens to the total resistance and the total current?

A parallel circuit is connected to a 12 V battery and draws a total current of 3.0 A. What is its total resistance, in ohms?

Match each part of the circuit rules to the correct statement.

Current in series

Potential difference in series

Potential difference in parallel

Current in parallel

Are the outlets and lights in a house wired in series or in parallel?

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