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3.2.5 Ohmic and non-ohmic resistors

Where resistance comes from

  1. A metal is made of a regular arrangement of positive ions, with free electrons able to move between them.
  2. When a potential difference is applied, the free electrons drift through the metal, forming the current.
  3. As they drift, the electrons collide with the ions, which slows them down and transfers energy to the ions.
    1. The energy transferred to the ions increases the thermal store of the metal, which is why a current heats a resistor.
  4. The more often the electrons collide with the ions, the greater the resistance of the metal.
  5. The ions are always vibrating, and the hotter the metal, the more strongly they vibrate, so the electrons collide with them more often.

Resistors with constant resistance

Definition

Ohmic conductor

A conductor whose resistance stays constant as the current through it changes, provided its temperature stays constant.

  1. If the temperature of a metal conductor stays the same, its ions keep vibrating by the same amount as the current changes.
  2. The rate of collisions for each electron therefore does not change, so the resistance stays constant.
  3. With a constant resistance, doubling the potential difference doubles the current, so the value of VI\dfrac{V}{I}IV​ is the same for every pair of readings.
  4. A conductor that behaves in this way is an ohmic conductor.
    1. Fixed resistors are made so that they stay close to room temperature for the currents they are designed to carry, so their resistance stays almost constant.
    2. A metal wire behaves as an ohmic conductor only while its temperature is kept constant, for example by keeping the current small.
  5. If a large current heats an ordinary resistor or wire, its resistance rises, so it stops behaving as an ohmic conductor.

Resistors with changing resistance

Definition

Non-ohmic component

A component whose resistance changes as the current through it changes.

Definition

Filament lamp

A lamp that gives out light because a thin metal filament inside it is heated to a very high temperature by the current.

  1. In some components, the resistance changes as the current changes, so they are non-ohmic.
  2. A filament lamp is the most important example.
    1. As the current through the filament increases, more energy is transferred to it every second, so its temperature rises, reaching over 2000 ∘C2000\ ^{\circ}\text{C}2000 ∘C when the lamp glows brightly.
    2. The hotter filament has ions that vibrate more, so the electrons collide with them more often.
    3. More frequent collisions mean the resistance of the filament increases as the current increases.
  3. Because its resistance rises, doubling the potential difference across a filament lamp less than doubles the current through it.
  4. An NTC thermistor also changes its resistance as the current changes, but in the opposite way.
    1. A large current warms the thermistor, and its resistance falls as its temperature rises, so the current rises faster than the potential difference.
  5. A diode has a very high resistance until the potential difference across it in the forward direction reaches about 0.6 V0.6\ \text{V}0.6 V, after which its resistance becomes very small.
  6. Non-ohmic does not mean that a component has no resistance, or that its resistance is large, but only that its resistance is not constant.

Testing whether resistance is constant

  1. To test a component, measure the current through it at several different potential differences.
  2. Calculate R=VIR = \dfrac{V}{I}R=IV​ for each pair of readings.
  3. If the values are the same, the component has a constant resistance over that range.
  4. If the values increase as the current increases, as for a filament lamp, the resistance is rising.
  5. If the values decrease as the current increases, as for a self-heating thermistor, the resistance is falling.
Example

Resistance of a filament lamp

  • A filament lamp gives these pairs of readings: 1.0 V1.0\ \text{V}1.0 V and 0.10 A0.10\ \text{A}0.10 A, 3.0 V3.0\ \text{V}3.0 V and 0.20 A0.20\ \text{A}0.20 A, and 6.0 V6.0\ \text{V}6.0 V and 0.25 A0.25\ \text{A}0.25 A.
R1=1.0 V0.10 A=10 Ω R_1 = \dfrac{1.0\ \text{V}}{0.10\ \text{A}} = 10\ \Omega R1​=0.10 A1.0 V​=10 Ω R2=3.0 V0.20 A=15 Ω R_2 = \dfrac{3.0\ \text{V}}{0.20\ \text{A}} = 15\ \Omega R2​=0.20 A3.0 V​=15 Ω R3=6.0 V0.25 A=24 Ω R_3 = \dfrac{6.0\ \text{V}}{0.25\ \text{A}} = 24\ \Omega R3​=0.25 A6.0 V​=24 Ω
  • The resistance rises from 10 Ω10\ \Omega10 Ω to 24 Ω24\ \Omega24 Ω as the current increases, so the lamp is non-ohmic.
  • The rise happens because the larger current makes the filament hotter, so its ions vibrate more and the electrons collide with them more often.
Example

Resistance of a fixed resistor

  • A fixed resistor gives 2.0 V2.0\ \text{V}2.0 V with 0.20 A0.20\ \text{A}0.20 A, and 4.0 V4.0\ \text{V}4.0 V with 0.40 A0.40\ \text{A}0.40 A.
R1=2.0 V0.20 A=10 Ω R_1 = \dfrac{2.0\ \text{V}}{0.20\ \text{A}} = 10\ \Omega R1​=0.20 A2.0 V​=10 Ω R2=4.0 V0.40 A=10 Ω R_2 = \dfrac{4.0\ \text{V}}{0.40\ \text{A}} = 10\ \Omega R2​=0.40 A4.0 V​=10 Ω
  • The resistance is the same at both currents, so the resistor behaves as an ohmic conductor over this range.
Common Mistake
  • Do not say the resistance of a lamp increases because the current is used up, because the cause is the rising temperature of the filament.
  • Do not say that the electrons vibrate more when a metal is heated, because it is the ions that vibrate more.
  • Do not describe a non-ohmic component as having no resistance, because non-ohmic only means that its resistance changes.
Exam technique

Explaining changing resistance

  • For an explanation of why the resistance of a filament lamp increases, write the full chain of cause and effect, with one link per step.
    • The current increases, so the temperature of the filament increases.
    • The ions vibrate more, so the electrons collide with them more often.
    • The more frequent collisions mean the resistance increases.
  • Missing out the ions or the collisions is the most common way to drop a mark on this explanation.
  • When you are given data, support your answer with at least two calculated resistance values.
Self review
  • Explain, in terms of ions and electrons, what causes resistance in a metal.
  • State the condition needed for a metal wire to have a constant resistance.
  • Explain why the resistance of a filament lamp increases as the current through it increases.
  • Describe how the resistance of an NTC thermistor changes as it warms up.
  • State what non-ohmic means.
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3.2.5 Ohmic and non-ohmic resistors Revision Guide

  1. GCSE
  2. /Physics
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Revision notes for OCR GCSE Physics 3.2.5 Ohmic and non-ohmic resistors: explanations and worked examples.

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