4.2.2 Ohm's Law & I-V Characteristics

• Ohm’s law states:

For a conductor at a constant temperature, the current through it is proportional to the potential difference across it

• Constant temperature implies constant resistance
• Ohm's law is represented in the equation below:

• Measuring the variation of current with potential difference through a fixed resistor will produce a straight line graph, such as the one below

Circuit for plotting graphs of current against voltage

• Since the gradient is constant, the resistance R of the resistor can be calculated by using 1 ÷ gradient of the graph
• An electrical component obeys Ohm’s law if its graph of current against potential difference is a straight line through the origin
  • A resistor does obey Ohm’s law
  • A filament lamp does not obey Ohm’s law

• This applies to any metal wires, provided that the current isn’t large enough to increase their temperature

I–V Characteristics

• 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
• For an ohmic conductor eg. a fixed resistor:
  • The I–V graph is a straight line through the origin

• For a non-ohmic conductor, such as
  • A semiconductor diode, the I–V graph is a horizontal line that goes sharply upwards
  • An LED (light-emitting diode), the I–V graph is similar to the semiconductor diode, since it is a specific diode that emits visible light
  • A filament lamp, the I–V graph has an 'S' shaped curve
  • A thermistor, the I–V graph is a curved line with increasing gradient through the origin

I–V characteristics for an ohmic conductor (e.g. resistor), semiconductor diode, filament lamp, LED and thermistor

Ohmic Conductor

• The I–V graph for an ohmic conductor at constant temperature e.g. a resistor is very simple:
  • The current is directly proportional to the potential difference
  • This is demonstrated by the straight-line graph through the origin

Semiconductor Diode

• The I–V graph for a semiconductor diode is slightly different. A diode is used in a circuit to allow current to flow only in a specific direction
• 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, it does not conduct and is called reverse bias
  • This is shown by a zero reading of current or potential difference on the left side of the graph which then goes steeply vertically down

• For an LED, the I–V graph is identical, except the sharp increase in p.d is further away from the origin as the frequency of the light increases

Filament Lamp

• The I–V graph for a filament lamp shows the current increasing at a proportionally slower rate than the potential difference
• This is because:
  • As the current increases, the temperature of the filament in the lamp increases
  • Since the filament is a metal, the higher temperature causes an increase in resistance
  • 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
• The filament lamp obeys Ohm's Law for small voltages

Thermistor

• The I–V graph for a thermistor is a shallow curve upwards
• The increase in the potential difference results in an increase in current which causes the temperature of the thermistor to rise
• As its temperature rises, its resistance decreases
  • This means even more current is able to flow through

• Since the current is not directly proportional to the potential difference (the graph is still curved), the thermistor does not obey Ohm's Law

      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 characteristic of a device that only has current in one direction e.g a semiconductor diode

• Therefore, the answer is C