Electric circuits · Model
Potential difference
A voltmeter never goes in a circuit. It goes across a part of one, and it answers a different question from an ammeter: not how much is flowing, but how hard it was pushed through there.
Start here
Every bulb has a number stamped on it.
A torch bulb says 2.5 V. A car headlamp says 12 V. A mains lamp says 230 V. Put the 2.5 V bulb on a 12 V battery and it flares once and dies; put the 12 V lamp on a single cell and nothing visible happens at all.
What is that number telling you?
It is the p.d. the maker designed it for — the push it expects to have across it. Give it much less and the filament never gets hot enough to glow properly; give it much more and the current through it is too big and the filament burns out. The rating is a specification, not a measurement of what the bulb is doing at any moment.
A cell does not make charge. It gives the charge energy, and pushes it out into the circuit carrying that energy. Potential difference — p.d. for short, often just called voltage — measures how much energy each bit of charge gives up between two points. It is measured in volts, written V.
Because it is a difference between two points, you can only ever measure it across something. That is why a voltmeter is connected in parallel with a component, with a lead to each side of it — not in the loop. An ammeter asks "how much is going past here?"; a voltmeter asks "how much energy was given up between here and there?"
In a series loop the battery's p.d. is shared out between the components: whatever the charge was given, it hands back on its way round, and the shares add up to the battery's value. The bigger share goes to whatever resists more. In parallel it is different — each branch is connected straight across the battery, so each branch gets the whole p.d.
At the bench · one series loop, one voltmeter, four places to put it
Move the voltmeter across.
Change a control to begin
A lamp and a second component in one loop. Change the battery, change the second component, and connect the voltmeter across each thing in turn.
Commit first. Two identical lamps sit in series on a 3.0 V battery. A voltmeter across the first lamp reads 1.5 V. What will it read across both lamps together?
The battery
The second component
The voltmeter goes across
The battery gives
—
—
Across the lamp
—
10 ohms
Across the second one
—
—
The voltmeter reads
—
—
The figure
What a rating means
A rating is not a measurement of the component. It is the p.d. the maker designed it to run at — the value at which it is as bright, or as loud, or as warm as it is meant to be.
| Component | Rating | Run under it | Run over it |
|---|---|---|---|
| Torch bulb | 2.5 V | Dim, or a dull red glow | One bright flash, then a broken filament |
| Car headlamp | 12 V | Yellow and weak — a flat battery looks like this | A much shorter life |
| Mains lamp | 230 V | Nothing you would notice on a cell | Fails at once |
| A single cell | 1.5 V | A battery's rating is what it supplies, not what it needs. Cells in series add: four of them give 6.0 V. | |
The last row is the one to watch. A component's rating says what it wants; a battery's rating says what it gives. Matching them is the whole job — and in a series loop what a component actually gets is only its share, not the battery's full value.
Writing it down · the shape of this relationship
The battery's push is shared out round a series loop
In parallel each branch gets the whole: a = b = V
V · potential difference of the battery · V
a · potential difference across the first component · V
b · potential difference across the second component · V
Worked example · one step at a time
A 4.5 V battery drives a lamp and a buzzer in series. A voltmeter across the lamp reads 1.8 V. What is the p.d. across the buzzer?
Step 0 of 5
Convert
4.5 V stays 4.5 V · 1.8 V stays 1.8 V
The battery and the voltmeter are both quoted in volts, so there is nothing to convert.
Formula
b = V − a
Cover b on the bar: the battery’s value with the other share taken away.
Insert
b = 4.5 V − 1.8 V
The whole is the battery, 4.5 V. The share you know is the lamp’s, 1.8 V.
Fine-tune
4.5 − 1.8 = 2.7
Volts take away volts leaves volts.
Answer
b = 2.7 V
Check it: 1.8 V and 2.7 V add to the 4.5 V of the battery.
Worked example · one step at a time
A 12 V supply drives two resistors in series. The voltmeter across the first reads 4500 mV. What is the p.d. across the second?
Step 0 of 5
Convert
4500 mV ÷ 1000 = 4.5 V
There are 1000 millivolts in a volt, so divide before you take anything away.
Formula
b = V − a
Cover b on the bar: the whole with the other share taken away.
Insert
b = 12 V − 4.5 V
The converted share goes in. The millivolt reading never does.
Fine-tune
12 − 4.5 = 7.5
Volts take away volts leaves volts.
Answer
b = 7.5 V
Take 4500 from 12 instead and you get − 4488 V, which no supply in the room could give.
Your turn · the same five steps
Your loop: the battery gives 3.0 V and the voltmeter across the lamp reads 1.50 V.
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
The five lines, marked
Convert
3.00 V stays 3.00 V · 1.50 V stays 1.50 V
The battery and the voltmeter are both in volts, so nothing changes.
Formula
b = V − a
Cover b on the bar: the whole with the other share taken away.
Insert
b = 3.00 V − 1.50 V
The whole is the battery; the share you know is the lamp’s.
Fine-tune
3.00 − 1.50 = 1.50
Volts take away volts leaves volts.
Answer
b = 1.50 V
Put the voltmeter across the second component and it reads 1.50 V.
The five lines give 1.50 V across the lamp, and 1.50 V + 1.50 V is the 3.0 V of the battery.
A 6.0 V battery drives a lamp and a buzzer in series. The voltmeter across the lamp reads 1500 mV.
This one needs the Convert line to do some work.
The five lines, marked
Convert
1500 mV ÷ 1000 = 1.5 V
There are 1000 millivolts in a volt, so divide before you take anything away.
Formula
b = V − a
Cover b on the bar: the whole with the other share taken away.
Insert
b = 6.0 V − 1.5 V
The converted share goes in. The millivolt reading never does.
Fine-tune
6.0 − 1.5 = 4.5
Volts take away volts leaves volts.
Answer
b = 4.5 V
Take 1500 from 6.0 instead and the buzzer comes out at − 1494 V.
The five lines give 4.5 V across the buzzer, and 1.5 V + 4.5 V is the 6.0 V of the battery.
Key fact
Potential difference is the energy each unit of charge gives up between two points, measured in volts (V) on a voltmeter connected across a component. Round a series loop the battery's p.d. is shared out and the shares add to it: V = a + b. In parallel every branch gets the whole of it.
Think again
“Voltage flows round the circuit and gets used up by each bulb.”
Nothing flows except charge. Potential difference is not a substance travelling anywhere — it is a difference between two places, like the drop between the top and the bottom of a hill. You would not say the height flows down the hill. The reason p.d. sounds like something being used up is that the shares do add to the battery's value, which is true and useful; but the thing being handed over is energy, and the thing carrying it is the current.
“A voltmeter goes in the circuit, like an ammeter.”
It cannot. A p.d. is a difference between two points, so a voltmeter needs a lead on each of them — it goes across a component, in parallel with it. Wire one into the loop instead and the circuit stops: a voltmeter is built to let almost no current through, which is exactly what makes it safe to hang across things without changing them. An ammeter is the opposite, built to let current through as freely as a piece of wire, which is why putting one across a battery is a short circuit.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
Three components sit in series on a 6.0 V battery. Voltmeters across the first two read 1.5 V and 3.0 V. What is the p.d. across the third?
Rung 2 · The one that catches people
A student measures 3.0 V across a battery and 3.0 V across the single lamp in its loop, and concludes the meter must be broken because the voltage should have been used up. What is right?
Rung 3 · Explain
A 3.0 V battery drives a lamp and a 20 ohm resistor in series. A voltmeter across the lamp reads 1.0 V. Explain what it reads across the resistor, what it reads across both together, and why the shares are not equal.
Rung 4 · Take it somewhere new
You have a 6 V battery and one 6 V bulb, and you need to run two of those bulbs at full brightness at the same time. Explain how you would wire them and why, and say what would go wrong with the other arrangement.
Key note
Potential difference measures how much energy each unit of charge gives up between two points, in volts (V). Because it is a difference, a voltmeter is connected across a component rather than in the loop. Round a series loop the battery's p.d. is shared out between the components and the shares add up to it, with the bigger share going to whatever resists more; in parallel each branch is connected straight across the battery and gets the whole of it. A component's rating is the p.d. it was designed to run at; a battery's rating is the p.d. it supplies.
Going further
One volt means one joule of energy given up by every coulomb of charge. That is the whole definition, and it explains something that sounds impossible: the ten thousand volts that jump from a door handle to your finger leave you unhurt, while a car battery at 12 V can weld metal. The volts say how much energy each bit of charge carries; the amps say how many bits go past each second. Damage needs both — and a power line has both, in enormous quantities, which is why you never go near one.
The sharing rule is a tool as well as a fact. Put two resistors in series across a supply and you can tap off any fraction of it you like from the point between them — a potential divider. It is how a volume slider, a joystick, a fuel gauge and a light-dependent sensor all work: something varies one resistance, the share of the voltage moves, and a circuit reads the change.
Before this lesson
Connects to
At GCSE this becomes
- Energy transferred = charge × p.d., the potential divider equation, and Kirchhoff's second law round a loop.
Where to next
Ask Mr Badmus AI
Got a series loop and one voltmeter reading, and want the rest?
The bench is a teaching model. Every component is treated as having a fixed resistance — lamp 10 ohms, resistor 20 ohms, wire link 0 ohms — so the shares are exact fractions; a real filament's resistance rises as it heats and a real wire link is not quite zero. The battery is treated as having no resistance of its own, and the voltmeter as drawing no current at all, so neither of them disturbs the reading. Cells are taken as 1.5 V each. Readings are rounded to two decimal places. The ratings in the figure are typical values, and a bulb marked with a p.d. is usually marked with a current or a power as well.
Lesson content © MrBadmusAI.