I-V Characteristics (DP IB Physics: SL)

• Ohm's law states that:

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

• 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 - it is a non-ohmic component

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 its current-voltage graph
  • Since resistance is R = V/I
  • R = 1/gradient 

ANSWER: D

Step 1: Write down the equation for the resistance R 

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

• • Gradient = I/V

R = 1/gradient

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

• The I-V characteristics of a circuit component is a graph of the current flowing through the component plotted against the voltage across it

Obtaining I-V Characteristics Experimentally

• 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

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 be plotted

I-V Graphs of Some Circuit Components

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

Ohmic Conductor

• Current is directly proportional to potential difference
• The 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

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