Electric circuits · Classify
Conductors and insulators
Conductor and insulator are not two kinds of thing. They are the two ends of one number, and that number runs across more than a million million.
Start here
One cable. Copper inside, plastic outside.
A lamp flex is a copper core in a plastic sheath, and the two materials are touching along its whole length. Charge pours down the copper and none of it comes out sideways through a millimetre of plastic.
Roughly how many times more does the plastic resist than the copper?
More than a million million. A short piece of copper is a few hundredths of an ohm; the same size of plastic is thousands of billions of ohms. Nothing else in school physics has a range like it, and that is what makes a cable possible: two materials touching, one of them an open road and the other so hard to cross that the difference is not even worth measuring.
A conductor is a material with charges free to move. In a metal those are the loose electrons every metal atom contributes to a shared pool; in salt water they are dissolved ions. An insulator has none free: every electron is locked into a bond, so there is nothing available to drift.
Because the difference is a matter of how many charges are free and how easily they move, it comes out as a difference in resistance — and the gap is not a small one. A metre of copper is a fraction of an ohm. A metre of dry wood is millions of ohms. A plastic ruler is millions of millions. Written out, the range covers more than fourteen zeros, which is why no single scale on a meter can show both ends.
There is no boundary line. Materials fill in the whole range: graphite conducts but poorly, salt water conducts but worse than any metal, tap water conducts far worse than salt water, damp wood conducts far better than dry wood. "Insulator" is a practical judgement — the current it lets through is too small to matter for the job — not a switch that is off.
At the bench · a test gap on a 6.0 V supply
Clip a specimen in and divide.
Change a control to begin
Two crocodile clips, a supply fixed at 6.0 V and an ammeter that can read from hundreds of amps down to millionths of a millionth. Change the specimen, and change how long a piece of it you clip in.
Commit first. A plastic ruler is clipped into the gap on 6.0 V. What does the ammeter read?
The specimen in the gap
How much of it
The ammeter reads
—
limited by the supply, not by the wire
—
So the resistance is
—
—
Which makes it
—
—
Compared with copper
—
The figure
Fourteen zeros, one axis
The same seven specimens, all 10 cm long, on an axis where every mark is a thousand times the one before it. A ruler scale could not draw this: on a scale that showed the plastic, every conductor would be at zero.
Read the gaps, not the bar lengths. Salt water resists about four hundred times as much as nichrome; tap water about a hundred times as much again; and the plastic ruler about four hundred thousand times as much as the dry wood beside it. Nothing on this axis is a switch that is off.
Writing it down · the shape of this relationship
Potential difference = current × resistance
The triangle
Cover the one you want
V = I × R
I = V ÷ R
R = V ÷ I
Cover V and I and R are left side by side — multiply them.
Cover I on the triangle: V sits over R, so you divide.
Cover R on the triangle: V sits over I, so you divide.
Two things side by side means multiply. One thing over another means divide.
V · potential difference across the test gap · V
I · current through the specimen in that gap · A
R · resistance of that specimen, at that length · Ω
1 Ω is 1 V for each 1 A
Worked example · one step at a time
The gap holds 10 cm of pencil lead on the 6.0 V supply, and the ammeter reads 0.20 A. What is its resistance?
Step 0 of 5
Convert
6.0 V stays 6.0 V · 0.20 A stays 0.20 A
The supply is in volts and the ammeter is in amps, so there is nothing to convert.
Formula
R = V ÷ I
Cover R on the triangle: V sits over I, so you divide.
Insert
R = 6.0 V ÷ 0.20 A
The p.d. is the supply across the gap; the current is what the ammeter passes.
Fine-tune
6.0 ÷ 0.20 = 30
Volts divided by amps leaves ohms.
Answer
R = 30 Ω
That is the resistance of 10 cm of pencil lead.
Worked example · one step at a time
A 12 cm strip of graphite on the 6.0 V supply, and the ammeter reads 30 mA. What is its resistance?
Step 0 of 5
Convert
30 mA ÷ 1000 = 0.030 A
There are 1000 milliamps in an amp, so divide before you go any further.
Formula
R = V ÷ I
Cover R on the triangle: V sits over I, so you divide.
Insert
R = 6.0 V ÷ 0.030 A
The converted current goes in. The milliamp reading never does.
Fine-tune
6.0 ÷ 0.030 = 200
Volts divided by amps leaves ohms.
Answer
R = 200 Ω
Put 30 in instead of 0.030 and you get 0.2 Ω — a thousand times too small, and copper-like.
Your turn · the same five steps
Your gap: 6.0 V across 10 cm of pencil lead (graphite), and the ammeter reads 200.0 mA.
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
Clip a specimen the ammeter can read into the gap at the bench, and these five lines will follow it.
The five lines, marked
Convert
200.0 mA ÷ 1 000 = 0.2 A
There are 1 000 milliamps in an amp, so divide before you go any further.
Formula
R = V ÷ I
Cover R on the triangle: V sits over I, so you divide.
Insert
R = 6.0 V ÷ 0.2 A
The supply is fixed, so only the current changes from specimen to specimen.
Fine-tune
6.0 ÷ 0.2 = 30
Volts divided by amps leaves ohms, however small the current is.
Answer
R = 30 Ω
That is the resistance of 10 cm of pencil lead (graphite), which is what makes it a conductor.
The five lines give 30 Ω for 10 cm of pencil lead (graphite).
A 15 cm strip of nichrome on the 6.0 V supply, and the ammeter reads 24 mA.
This one needs the Convert line to do some work.
The five lines, marked
Convert
24 mA ÷ 1000 = 0.024 A
There are 1000 milliamps in an amp, so divide before you go any further.
Formula
R = V ÷ I
Cover R on the triangle: V sits over I, so you divide.
Insert
R = 6.0 V ÷ 0.024 A
The converted current goes in. The milliamp reading never does.
Fine-tune
6.0 ÷ 0.024 = 250
Volts divided by amps leaves ohms.
Answer
R = 250 Ω
Put 24 in instead of 0.024 and you get 0.25 Ω — a thousand times too small.
The five lines give 250 Ω for 15 cm of nichrome.
Key fact
A conductor has charges free to move — loose electrons in a metal, dissolved ions in salt water — and a low resistance. An insulator has none free and a resistance millions of millions of times higher. The two are the ends of one continuous range, not two separate kinds of material.
Think again
“An insulator blocks electricity completely — absolutely nothing gets through.”
Not quite nothing. Put 6 V across a plastic ruler and a current does flow: about three millionths of a millionth of an amp. It is too small for any school meter to see and far too small to do anything, which is exactly why we call the plastic an insulator — but the word describes how little, not none. The distinction matters at high voltages, where "too small to matter" stops being true: this is why overhead power lines hang from ceramic insulators the size of a bucket rather than a strip of tape.
“Materials are either conductors or insulators, with nothing in between.”
The middle of the range is crowded. Pencil lead conducts well enough to light a bulb and badly enough to get hot doing it. Tap water conducts a hundred times worse than salt water and a thousand times better than dry wood. Damp wood is a different material, electrically, from dry wood. And silicon sits deliberately in the middle: a semiconductor whose resistance can be controlled, which is the entire basis of every chip ever made.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate and classify
A specimen is clipped across a 6.0 V supply and the ammeter reads 0.15 A. What is its resistance, and how would you classify it?
Rung 2 · The one that catches people
A student clips a plastic ruler across 6 V, sees the ammeter stay on zero, and concludes that the resistance of plastic is infinite. What is right?
Rung 3 · Explain
Explain why a lamp flex is made of copper inside and plastic outside, using resistance figures and the idea of free charges.
Rung 4 · Take it somewhere new
A wooden ladder is often said to be safer than an aluminium one near overhead cables, but electricians are taught that a wet wooden ladder is not safe at all. Explain both statements using resistance.
Key note
A conductor has charges free to move and a low resistance; an insulator has almost none free and a resistance millions of millions of times higher. In a metal the free charges are loose electrons; in salt water they are dissolved ions. The difference is measured, not declared: put a known p.d. across a specimen, read the current, divide. The results fill a continuous range from hundredths of an ohm to millions of millions of ohms, with graphite, salt water, tap water and damp wood spread across the middle, so "insulator" means the current is too small to matter rather than that there is none.
Going further
Silicon is the interesting one. On its own it is a poor conductor, but add a few atoms of another element per million — doping — and its resistance drops by orders of magnitude in a way you can design. Put two differently doped regions side by side and you have a component that conducts one way and not the other; put three together and you have a switch with no moving parts. Every transistor in every chip is that trick, repeated. The whole of computing rests on a material that refused to be either a conductor or an insulator.
At the other extreme, some metals stop resisting altogether. Cool mercury below about 4 kelvin and its resistance does not merely fall, it becomes zero: a current started in a loop of it will still be going years later. Superconductors are how MRI scanners make their enormous magnetic fields, and the reason those machines need a tank of liquid helium to work at all.
Before this lesson
Connects to
At GCSE this becomes
- Resistivity as a property of the material rather than the sample, semiconductors and doping, and thermistors as resistance that reports temperature.
Where to next
Ask Mr Badmus AI
Got a current and a p.d. and want to know whether it counts as a conductor?
Mains electricity is not a bench supply, and a scorched socket, a cable with the copper showing or a plug that gets hot is worth telling an adult about the same day — never test it yourself. If there is no one at home you can tell, Childline is free on 0800 1111, at any hour, and you do not have to give your name.
The bench is a teaching model. The seven resistances are typical values for a 10 cm specimen and not measurements of particular objects: real samples vary widely with thickness, purity, temperature and, for wood and water, how much moisture and dissolved salt they contain. Lengthening a specimen tenfold is taken to multiply its resistance by ten, which holds for a sample of even cross-section. The supply, leads and meter are treated as having no resistance, so the reading is the specimen's alone. The copper state deliberately reports no current: a bare copper wire across a supply is a short circuit, and the current then depends on what the supply can deliver rather than on the wire, so there is no honest figure for the meter to show. The boundary drawn on the figure is a convenience and not a real dividing line.
Lesson content © MrBadmusAI.