Resistance & Ohm's Law
Resistance is often misunderstood as a "law" every component must obey. It isn't. Resistance is a definition that works for anything you connect into a circuit; Ohm's law is a special, limited case of how that resistance can behave.
Resistance as a general definition
The previous lesson introduced resistance as the ratio of potential difference to current:
This isn't a law of physics, and it doesn't claim anything about how $V$ and $I$ behave as you change one of them. It's simply a definition — a way of quantifying, for any conductor, how much potential difference is needed to drive a given current through it. You can calculate a resistance for a copper wire, a filament lamp, a diode, a thermistor, a length of nichrome — anything that carries current — by measuring $V$ and $I$ simultaneously and dividing. The definition doesn't care what the component is or how it behaves as conditions change.
Ohm's law: a special case, not a universal rule
"Ohm's law" sounds like it should be a fundamental law every circuit component obeys, the way Newton's laws apply to every mechanical system. It isn't. Ohm's law describes the behaviour of a particular, limited class of conductors, under a particular condition.
Properly stated: for a conductor kept at constant physical conditions — most importantly, constant temperature — the current through it is directly proportional to the potential difference across it.
Direct proportionality is the crucial detail: double $V$ and you double $I$, so $R = V/I$ stays exactly the same no matter what value of $V$ you test. Plot $I$ against $V$ for a conductor obeying Ohm's law and you get a straight line through the origin: constant resistance at every point.
A conductor that behaves this way is called ohmic. Plenty of components — a filament lamp, a diode — are decidedly not ohmic, since their resistance changes substantially as current flows (mainly due to temperature, in the lamp's case). Their $V$ and $I$ are still related — you can always calculate a resistance at any operating point using $R=V/I$ — it's just that this resistance isn't constant, so $I \propto V$ doesn't hold. "Ohmic" describes how a specific conductor happens to behave under specific conditions, not a law circuits must follow.
$R = V/I$ always works, for any component, at any single instant — it's a definition. $I \propto V$ only works for ohmic conductors held at constant temperature — it's a specific behaviour. Every ohmic conductor obeys $R=V/I$, but not every conductor that obeys $R=V/I$ is ohmic.
Idealised meters: why ammeters and voltmeters are treated specially
Whenever you calculate currents and potential differences around a circuit at this level, you'll almost always be told — or expected to assume — that the meters involved are ideal. Specifically:
- An ammeter, which measures current, is treated as having zero resistance.
- A voltmeter, which measures potential difference, is treated as having infinite resistance.
This follows from what each meter must do without disturbing the circuit it's measuring. An ammeter is connected in series, directly in the path of the current. If it had significant resistance of its own, it would add to the circuit's total resistance and reduce the very current it's measuring. Zero resistance means it can be inserted without altering the current at all.
A voltmeter is connected in parallel across a component. If it had finite resistance, it would provide charge carriers an alternative path, drawing current away from the component and changing the circuit's behaviour. Infinite resistance means, in effect, no current flows through the voltmeter branch, so it measures potential difference without diverting current or disturbing the circuit.
Real meters don't hit these ideals exactly — a real ammeter has some small resistance, a real voltmeter draws some tiny current — but well-designed meters get close enough that treating them as ideal is safe unless a question states a meter resistance.
Key takeaways
- Resistance is defined as $R = V/I$, and this definition applies to any conductor at all, ohmic or not.
- The ohm is derived directly from this definition: $1\,\Omega = 1\,\text{V}\,\text{A}^{-1}$.
- Ohm's law is a specific behaviour, not a universal rule: for a conductor at constant temperature, $I \propto V$, so resistance stays constant as $V$ and $I$ change.
- A conductor that obeys this proportionality is called ohmic; many common components (filament lamps, diodes) are not ohmic because their temperature or other conditions change with current.
- Ammeters are idealised as having zero resistance so they don't reduce the current they're placed in series to measure.
- Voltmeters are idealised as having infinite resistance so they don't draw current away from the component they're placed in parallel across.