Resistance and Ohm's Law

We now have current (I), charge (Q), drift velocity (v), EMF (ε) and potential difference (V). It is time to link them together with the single most famous equation in circuit analysis: V = IR, better known as Ohm's law.

But Ohm's law is not just "V = IR". It is a statement about a particular class of materials — ohmic conductors — whose resistance stays constant regardless of the current. The equation V = IR itself is simply the definition of resistance and applies to any component, ohmic or not.

Confusing the definition with the law is the single most common A-Level electricity mistake. This lesson will fix it.

OCR A-Level Physics A Module 4.2.2 (Energy, power and resistance).

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Defining Resistance

The electrical resistance R of a component is defined as the ratio of the potential difference V across it to the current I flowing through it:

R = V / I

• R is measured in ohms (Ω), named after Georg Ohm (1789–1854).
• 1 Ω = 1 V / 1 A = 1 V A⁻¹

Rearranged, this becomes the familiar V = IR form used in almost every calculation. A third form, I = V/R, is useful when you want to predict the current drawn by a known resistor.

Worked Example 1

A resistor of 220 Ω has a pd of 6.0 V across it. What is the current?

• I = V / R = 6.0 / 220 = 0.0273 A ≈ 27 mA

Worked Example 2

A current of 0.50 A flows through a wire when a pd of 12 V is applied. What is its resistance?

• R = V / I = 12 / 0.50 = 24 Ω

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Ohm's Law — The Actual Statement

Ohm's Law: The current through a metallic conductor is directly proportional to the potential difference across it, provided the temperature and other physical conditions are constant.

In symbols:

I ∝ V (at constant temperature)

which is equivalent to saying R is a constant, independent of V or I. Components that satisfy Ohm's law are called ohmic conductors. A metal wire held at constant temperature is the classic example.

If you draw a graph of I against V for an ohmic conductor, you get a straight line through the origin. The gradient is 1/R, or equivalently R = V/I is the inverse gradient.

Exam Tip: OCR mark schemes are strict on the phrase "at constant temperature" (or "provided physical conditions are constant"). Leaving it out can cost a mark even if the rest of the statement is correct.

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Ohm's Law vs V = IR — The Crucial Distinction

Statement	Meaning	Applies to
R = V / I	Definition of resistance	All components
V = IR with R constant (Ohm's Law)	Physical law about ohmic materials	Only ohmic conductors

Every component has a resistance — you can always compute R = V/I at any operating point. But only ohmic components have a constant R. For non-ohmic components (filament lamp, diode, thermistor), R changes as the conditions change, so there is a different R at every point on the I-V curve.

Put another way: Ohm's law is the experimental observation that for some materials, a graph of I against V is a straight line through the origin. For others — diodes, lamps, thermistors — the graph is curved, and those materials are non-ohmic.

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Non-Ohmic Behaviour — A Preview

In the next lesson we will look at the I-V characteristics of four important components:

• Ohmic resistor — straight line through the origin.
• Filament lamp — curve, because the filament heats up and its resistance rises.
• Diode — very non-linear, switches on at about 0.6–0.7 V (for silicon).
• NTC thermistor — curve, because carrier density rises with temperature.
• LDR — resistance drops in bright light.

For any of these, V = IR still gives the correct resistance at a particular operating point, but R is not a constant. So if you are asked to calculate R for a filament lamp at a specific V and I, you can still use R = V/I — you just cannot assume the answer applies at a different V.

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Worked Example 3 — Straight Line on I-V