Electric Current and Ohm's Law

Lessons

Senior 1 · Physics

Electric Current and Ohm's Law

5 lessons

Lesson 2 of 5

Simple Circuits, Their Components and Electrical Safety

25 min

One lamp goes out: why do the others stay on?

When one bulb in your house blows, the others keep shining. But on some cheap strings of decorative lights, one broken bulb makes the whole string go dark. The difference is not in the bulbs; it is in how they are connected. Physicists and electricians plan these connections with circuit diagrams, drawn with standard symbols that every electrician in the world can read.

Circuit symbols

Symbol	Component	What it does
	cell	gives energy to the charges; the long thin plate is the positive terminal
	battery	two or more cells joined in series
	lamp (bulb)	changes electrical energy into light and heat
	switch (open)	breaks the circuit: no current flows
	switch (closed)	completes the circuit
	resistor	a fixed resistance that limits the current
	variable resistor (rheostat)	a resistance you can change, for example to dim a lamp
	fuse	a thin wire that melts and breaks the circuit if the current is too big
	ammeter	measures current; connected in series
	voltmeter	measures potential difference; connected in parallel
	galvanometer	detects very small currents and their direction
	wires joined (junction)	a dot shows that wires are connected
	wires crossing, not joined	no dot: the wires cross without touching

Definition

A circuit diagram is a drawing of an electric circuit that uses standard symbols for the components and straight lines for the connecting wires. A component is any part joined into a circuit: a cell, lamp, switch, resistor, meter and so on.

Series circuits

Figure 2.1: Two lamps in series. The charges have only one path, so they pass through both lamps in turn.

Build the circuit with two identical torch lamps. Both glow, but more dimly than one lamp alone would. Unscrew one lamp and BOTH go out, because the only path is broken. In a series circuit:

the current is the same at every point: $I = I_{1} = I_{2}$ ;
the p.d. of the supply is shared between the components: $V = V_{1} + V_{2}$ ;
one switch controls everything, and one break stops everything.

Parallel circuits

Figure 2.2: Two lamps in parallel. The current splits at the junction; each lamp has its own path and its own switch.

Now connect each lamp in its own branch. Both glow brightly, as brightly as one lamp alone. Open switch S₁ and lamp L₁ goes out, but L₂ stays lit. In a parallel circuit:

each branch has the same p.d. as the supply: $V = V_{1} = V_{2}$ ;
the current from the supply splits at a junction, and the branch currents add up to it: $I = I_{1} + I_{2}$ ;
each branch can be switched on and off on its own.

This is why houses are wired in parallel: every lamp and socket gets the full $230\,\mathrm{V}$ and can be used independently.

	Series	Parallel
Paths for the current	one	two or more
Current	the same everywhere	shared: $I = I_{1} + I_{2}$
Potential difference	shared: $V = V_{1} + V_{2}$	the same across each branch
If one lamp breaks	all go out	the others stay on
Brightness of identical lamps	dimmer as you add lamps	each as bright as one lamp alone
Example	cells in a torch; a switch and the lamp it controls	lamps and sockets in a house

Worked example 1: two lamps in series

Two identical lamps are connected in series to a $6.0\,\mathrm{V}$ battery. The current from the battery is $0.30\,\mathrm{A}$ . Find the current through each lamp and the p.d. across each lamp.

In series the current is the same everywhere: $0.30\,\mathrm{A}$ through each lamp.

The p.d. is shared, equally because the lamps are identical: $V_1 = V_2 = \frac{6.0\,\mathrm{V}}{2} = 3.0\,\mathrm{V}$ . Check: $3.0 + 3.0 = 6.0\,\mathrm{V}$ .

Worked example 2: two lamps in parallel

Two different lamps are connected in parallel to a $3.0\,\mathrm{V}$ battery. One takes $0.20\,\mathrm{A}$ and the other $0.30\,\mathrm{A}$ . Find the current from the battery and the p.d. across each lamp.

I = I_1 + I_2 = 0.20 + 0.30 = 0.50\,\mathrm{A}

Each branch is connected directly across the battery, so each lamp has $3.0\,\mathrm{V}$ across it.

Worked example 3: cells in series

A torch holds three $1.5\,\mathrm{V}$ cells end to end, the + terminal of each touching the − terminal of the next. What p.d. do they give?

V = 1.5 + 1.5 + 1.5 = 4.5\,\mathrm{V}

If one cell is put in the wrong way round, it cancels one of the others: $1.5 + 1.5 - 1.5 = 1.5\,\mathrm{V}$ , and the torch is dim.

Warning

Short circuit. A wire joined straight across the terminals of a cell or battery, with no lamp or other component in the path, gives a very large current. The wire and the cell get hot, the cell runs flat quickly, and a car battery can melt the wire and start a fire. Never connect a wire directly across a supply.

Safety with electrical appliances

The $230\,\mathrm{V}$ mains supply can kill. The human body conducts, and a current of about $0.1\,\mathrm{A}$ through the chest can stop the heart pumping properly. Damp skin conducts far better than dry skin, which is why water and electricity are such a dangerous mix. Homes are protected in three ways:

A fuse or a circuit breaker in each circuit cuts off the current if it becomes too large, for example in a short circuit or when too many appliances are plugged in, before the wires overheat and start a fire. Most Rwandan homes have their circuit breakers in the distribution board next to the prepaid (Cash Power) meter.
The earth wire joins the metal case of an appliance, such as a kettle or a fridge, to the ground. If a live wire works loose and touches the case, a large current flows to earth and trips the circuit breaker, instead of passing through the person who touches the case.
Insulation: plastic covers on cables, plugs and switches, and appliances marked "double insulated", keep your fingers away from live metal.

Worked example 4: choosing a fuse

An electric iron takes a current of $4.3\,\mathrm{A}$ . Fuses are sold rated at $3\,\mathrm{A}$ , $5\,\mathrm{A}$ and $13\,\mathrm{A}$ . Which should protect it?

$3\,\mathrm{A}$ is less than the normal current, so the fuse would melt as soon as the iron is switched on.
$13\,\mathrm{A}$ would let a dangerous fault current flow for a long time before melting.
Choose $5\,\mathrm{A}$ : the smallest rating just above the normal current.

Warning

Electrical safety at home

Never touch switches, plugs or appliances with wet hands, and keep water, drinks and wet cloths away from sockets.
Do not overload a socket with many adapters and extension leads: the plug and the wires overheat.
Replace damaged cables and cracked plugs; never repair a cable with sticky tape.
Pull out a plug by holding the plug, not by pulling the cable.
Never push anything except a plug into a socket, and switch off at the main switch before changing a bulb.
Keep away from fallen power lines and never climb pylons or electricity poles; report damage to REG.
If someone is receiving a shock, do not touch them: switch off the supply first, or push them free with a dry wooden stick.

Tip

Series: Same current, Split voltage. Parallel: same p.d., currents Plus up. And in any diagram, a dot means joined; no dot means crossing.

Try it

Build both circuits with torch lamps and cells, or on screen with PhET: Circuit Construction Kit: DC (version 1.4.2). Add a third lamp to each circuit and compare how the brightness changes; then break one wire in each and see which lamps go out.

Series and parallel circuits (FuseSchool). Watch how the current and the voltage behave in each kind of circuit, and why homes are wired in parallel.

✦

Practice

Draw the circuit symbols for: a cell, a lamp, an open switch, a resistor, an ammeter and a voltmeter.
Draw a circuit diagram with a battery, a switch and two lamps in series.
Two identical lamps in series are connected to a $12\,\mathrm{V}$ battery, and the current is $0.50\,\mathrm{A}$ . Find the current through each lamp and the p.d. across each.
Three lamps in parallel take currents of $0.10\,\mathrm{A}$ , $0.25\,\mathrm{A}$ and $0.40\,\mathrm{A}$ from a $6.0\,\mathrm{V}$ supply. Find the total current, and the p.d. across each lamp.
A kettle takes $8.7\,\mathrm{A}$ . Which fuse should it have: $5\,\mathrm{A}$ , $10\,\mathrm{A}$ or $30\,\mathrm{A}$ ? Explain.
Give three rules for using electrical appliances safely at home, and explain the reason for each.
Byiringiro says, "Houses should be wired in series, because then one switch at the door turns everything off." Evaluate his idea.

Show answersHide answers

See the table of symbols at the start of this lesson.
One loop: battery, switch, lamp, lamp, back to the battery, with no junctions.
Current $0.50\,\mathrm{A}$ through each (series); p.d. $\frac{12}{2} = 6.0\,\mathrm{V}$ across each (identical lamps share it equally).
$I = 0.10 + 0.25 + 0.40 = 0.75\,\mathrm{A}$ ; each lamp has the full $6.0\,\mathrm{V}$ across it.
$10\,\mathrm{A}$ : the smallest rating above the normal current. A $5\,\mathrm{A}$ fuse would melt in normal use; a $30\,\mathrm{A}$ fuse would let a dangerous fault current flow.
Any three, for example: dry hands (water conducts, so a current could pass through you); no overloaded sockets (the wires overheat and can start a fire); replace damaged cables (bare live wires can be touched); pull the plug, not the cable (pulling loosens the wires inside).
A poor idea. In series, every appliance would share the $230\,\mathrm{V}$ , so none would work properly; one broken lamp would turn off the whole house; and you could not use one appliance without all the others. A main switch in the distribution board already turns everything off in a parallel system.

Key points

Circuit diagrams use standard symbols; a dot marks a junction.
Series: one path, the same current, shared p.d. Parallel: separate branches, the same p.d., and $I = I_{1} + I_{2}$ .
Fuses and circuit breakers, the earth wire and insulation protect us from the $230\,\mathrm{V}$ mains; water and damaged cables are the great dangers.

Sources and credits

21.1: Resistors in Series and Parallel, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
20.6: Electric Hazards and the Human Body, from College Physics (1st edition) by Paul Peter Urone and Roger Hinrichs, OpenStax, hosted by LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: Circuit breaker 2 pole on DIN rail.JPG by Kae, Wikimedia Commons, licensed under CC BY-SA 3.0.
Circuit Construction Kit: DC (version 1.4.2). Simulation by PhET Interactive Simulations, University of Colorado Boulder, licensed under CC BY 4.0 (https://phet.colorado.edu)
Video: Series and Parallel Circuits | Electricity | Physics | FuseSchool, FuseSchool - Global Education, embedded from YouTube.

The circuit diagrams, the symbol table, the worked examples, the safety guidance for Rwandan homes and the practice exercises are written by Ganzaa.

1One lamp goes out: why do the others stay on?

2Circuit symbols

3Series circuits

4Parallel circuits

5Safety with electrical appliances

6Try it