I–V Graphs (OCR Gateway GCSE Physics: Combined Science)

• As the potential difference (voltage) across a component is increased, the current also increases (by Ohm’s law)
• The precise relationship between voltage and current is different for different components and can be shown on an I-V graph
• • This is known as the I-V characteristic of the component
• Circuit components can have I-V characteristic graphs that are linear or non-linear
  • In maths, linear means the graph is a straight line

• To know whether a circuit element is linear or non-linear, check whether its I-V graphs is a straight line or not
  • Linear components have an I-V graph that is a straight line through the origin
  • Non-linear components have an I-V graph that is not a straight line

• Linear components are said to obey Ohm's Law and have a constant resistance, whilst non-linear do not
• Some components may be linear at low currents, then become non-linear as the current increases (and therefore a change in temperature)
  • For example, a fixed resistor at room temperature is linear, but when it becomes very hot it will become non-linear

Linear and non-linear I-V graphs

• Components with linear I-V characteristics include:
  • Fixed resistors
  • Wires
  • Heating elements

• Components with non-linear I-V characteristics include:
  • Filament lamps
  • Diodes & LEDs
  • LDRs
  • Thermistors

Fixed Resistors

• The current through a fixed resistor increases as the potential difference across it increases
• In other words, current is directly proportional to the potential difference for a fixed resistor
• An I-V graph shows that the line is straight and goes through the origin, as shown in the I-V graph below:

I-V graph for a fixed resistor. The current is directly proportional to the potential difference as the graph is a straight line through the origin

• This relationship is true because the resistance of a fixed resistor is constant

---

Filament Lamps

• For a filament lamp, current and potential difference are not directly proportional
  • This is because the resistance of the filament lamp increases as the temperature of the filament increases

• The I–V graph for a filament lamp shows the current increasing at a proportionally slower rate than the potential difference

I-V graph for a filament lamp

• This is because:
  • As the current increases, the temperature of the filament in the lamp increases
  • The higher temperature causes the atoms in the metal lattice of the filament to vibrate more
  • This causes an increase in resistance as it becomes more difficult for free electrons (the current) to pass through
  • Resistance opposes the current, causing the current to increase at a slower rate

• Where the graph is a straight line, the resistance is constant
• The resistance increases as the graph curves
• Reversing the potential difference reverses the current and makes no difference to the shape of the curve

---

Diodes

• A diode allows current to flow in one direction only
  • This is called forward bias

• In the reverse direction, the diode has very high resistance, and therefore no current flows
  • This is called reverse bias

I-V graph for a semiconductor diode

• The I–V graph for a diode is slightly different:
  • When the current is in the direction of the arrowhead symbol, this is forward bias
    • This is shown by the sharp increase in potential difference and current on the right side of the graph

  • When the diode is switched around, this is reverse bias
    • This is shown by a zero reading of current or potential difference on the left side of the graph

Answer: C

• The I-V graph X is linear
  • This means the graph has a constant gradient. I/V and the resistance is therefore also constant (since gradient = 1/R)
  • This is the I-V graph for a conductor at constant temperature e.g. a resistor

• The I-V graph Y starts with zero gradient and then the gradient increases rapidly
  • This means it has infinite resistance at the start which then decreases rapidly
  • This is characters of a device that only has current in one direction e.g a semiconductor diode

• Therefore the answer is C