IBPhysicsHLRevision NotesThe Particulate Nature of MatterCurrent & CircuitsI-V Characteristics

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I-V Characteristics (HL IB Physics)

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Ohm's Law

  • Ohm's law states that:

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

  • It is defined by the equation:

V space equals space I R

  • Where:
    • V = potential difference (V)
    • I = current (A)
    • R = resistance (Ω)
  • An electrical component obeys Ohm’s law if its graph of current against potential difference is a straight line through the origin
    • A fixed resistor obeys Ohm’s law i.e. it is an ohmic component
    • A filament lamp does not obey Ohm’s law i.e. it is a non-ohmic component

Ohm's law graph, downloadable AS & A Level Physics revision notes

The current-voltage graph for a fixed resistor is a straight line through the origin. The fixed resistor is an ohmic component

  • The resistance of an ohmic component can be calculated from the gradient of a current-voltage graph, since resistance is equal to

R space equals space V over I

  • If current I is on the y-axis and potential difference V is on the x-axis, then R space equals space fraction numerator space 1 over denominator g r a d i e n t end fraction
  • If potential difference V is on the y-axis and current I is on the x-axis, then R space equals space g r a d i e n t
  • Any metal conductor at a constant temperature can be considered an ohmic device
    • This is likely to be a fixed resistance
  • Non-ohmic devices include:
    • Lamps
    • LEDs
    • Thermistors

Worked example

The current flowing through a component varies with the potential difference V across it as shown.

WE - ohms law question image(1), downloadable AS & A Level Physics revision notes

Which graph best represents how the resistance R varies with V?WE - ohms law question image(2), downloadable AS & A Level Physics revision notes

Answer: D

Step 1: Write down the equation for the resistance R 

R space equals space V over I

Step 2: Link the resistance to the gradient of the graph 

g r a d i e n t space equals fraction numerator space I over denominator V end fraction space space space space space rightwards double arrow space space space space space R space equals space fraction numerator space 1 over denominator g r a d i e n t end fraction

Step 3: Identify the gradient of different sections of the graph and use it to deduce what happens to the resistance   

  • The first straight section of the graph has a constant gradient
    • So the resistance remains constant
  • The second section is curved and the steepness of the line increases, so the gradient increases
    • So the resistance decreases

Step 4: Identify the correct graph out of the four proposed 

  • Constant resistance is indicated by a straight horizontal line
    • So either C or D are correct
  • Decreasing resistance is indicated by a line curving downwards
    • So only D is correct

Examiner Tip

When solving problems about Ohm's law you will often deal with graphs. You need to be confident in identifying and calculating their gradients.

  • In maths, the gradient is the slope of the graph (i.e. fraction numerator r i s e over denominator r u n end fraction)
  • The graphs below show a summary of how the slope of the graph represents the gradient

 

Different gradients, downloadable AS & A Level Physics revision notes

Although the Ohm's law equation is not given on your data sheet, you can see it is just rearranging R space equals fraction numerator space V over denominator I end fraction to make V the subject.

I-V Characteristics

  • The Ohmic and non-Ohmic behaviour of an electrical conductor can be deduced by looking at its I-V (current-voltage) characteristics
    • This is usually plotted as a graph showing the variation of current against voltage
  • The relation between potential difference across an electrical component (e.g. a fixed resistor) and current can be investigated through a circuit such as the one below

Ohm's law experiment, downloadable AS & A Level Physics revision notes

Circuit for plotting graphs of current against voltage. The component being investigated here is a fixed resistor

  • By adjusting the resistance on the variable resistor:
    • The current in the circuit will change
    • For each value of the current I, the potential difference V can be recorded

  • A graph of current against potential difference can then be plotted

I-V characteristics of common conductors

  • Common ohmic conductors include
    • Wires (at constant temperature)
    • Resistors
  • Common non-ohmic conductors include
    • Semiconductor diodes e.g. LEDs
    • Filament lamp
    • Thermistors & light-dependent resistors (LDRs)

IV conductor and diode graphs, downloadable AS & A Level Physics revision notes

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

Resistor

  • A resistor is an example of an Ohmic resistor
    • This means the current is directly proportional to the potential difference
    • Its I-V graph is a straight line through the origin

Semiconductor Diode

  • When the current is in the direction of the arrowhead symbol, the diode is said to be forward-biased
    • There is a sharp increase in current
    • This is shown on the right side of the graph

  • When the diode is switched around, it does not conduct and it is said to be reverse biased
    • The current through the diode is zero
    • This is shown on the left side of the graph

  • The diode is a non-ohmic component
    • Its I-V graph is not a straight line through the origin

  • A specific type of diode is an LED
    • The I-V characteristic graphs looks the exact same for this

Filament lamp IV graph, downloadable AS & A Level Physics revision notes

I–V characteristics for a filament lamp

Filament Lamp

  • For very small voltages, the filament lamp behaves as an ohmic component
    • The middle section of the graph (around zero voltage) is straight and passes through the origin

  • As voltage increases:
    • More current flows through the filament lamp and the temperature of the filament in the lamp increases
    • The higher the temperature of the filament, the higher its resistance
    • Since resistance opposes current, the current flows through the filament at a slower rate 
    • This is shown by the curved section of the graph

  • For slightly higher voltages, the filament lamp is non-ohmic 
    • The I-V graph is a curve with decreasing gradient

Examiner Tip

Make sure you're confident in drawing the I–V characteristics for different components, as you may be asked to sketch these from memory or to identify those given in exam questions

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.