Potential Dividers (CIE IGCSE Physics)

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• When two resistors are connected in series, the potential difference across the power source is shared between them

A potential divider splits the potential difference of a power source between two components

 

• The potential difference across each resistor depends upon its resistance:
  • The resistor with the largest resistance will have a greater potential difference than the other one
  • If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share

 

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• A potentiometer is a single component that (in its simplest form) consists of a coil of wire with a sliding contact, midway along it

 

A potentiometer is a kind of variable resistor

 

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• The sliding contact has the effect of separating the potentiometer into two parts – an upper part and a lower part – both of which have different resistances

Moving the slider (the arrow in the diagram) changes the resistances (and hence potential differences) of the upper and lower parts of the potentiometer

 

• If the slider in the above diagram is moved upwards, the resistance of the lower part will increase and so the potential difference across it will also increase

 

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• When two resistors are connected in series, through Kirchhoff’s Second Law, the potential difference across the power source is divided between them
• Potential dividers are circuits which produce an output voltage as a fraction of its input voltage
• Potential dividers have two main purposes:
  • To provide a variable potential difference
  • To enable a specific potential difference to be chosen
  • To split the potential difference of a power source between two or more components

• Potential dividers are used widely in volume controls and sensory circuits using LDRs and thermistors
• Potential divider circuits are based on the ratio of voltage between components. This is equal to the ratio of the resistances of the resistors in the diagram below, giving the following equation:

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Potential divider diagram and equation

• Where:
  • R₂ is the numerator and the resistance of the resistor over V_out 
  • R₁ is the other resistance in series
  • V_out is the output potential difference
  • V_in is the input potential difference
• The potential divider equation can also be written:

• Where this time:
  • R₁ is the numerator and the resistance of the resistor over V_out 
  • R₂ is the other resistance in series
• Whichever notation you use you will obtain the same answer
  • The numerator has to be the resistance of the resistor over V_out

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• The input voltage V_in is applied to the top and bottom of the series resistors
• The output voltage V_out is measured from the centre to the bottom of resistor R₂
• The potential difference V across each resistor depends upon its resistance R:
  • The resistor with the largest resistance will have a greater potential difference than the other one from V = IR
  • If the resistance of one of the resistors is increased, it will get a greater share of the potential difference, whilst the other resistor will get a smaller share

• In potential divider circuits, the p.d across a component is proportional to its resistance from V = IR