Notes: Resistors in Parallel | Physics for Grade 10 PDF Download

Deriving the Equation for Resistors in Parallel

• In a parallel circuit, the reciprocal of the combined resistance of two or more resistors is the sum of the reciprocal of the individual resistances
• In a parallel circuit:
  • The current is the split at the junction (and therefore between resistors)
  • The potential difference is the same through all resistors
• The equation for combined resistors in parallel is derived using Kirchhoff’s laws:
  

Resistors in Parallel

• When two or component are connected in parallel:
  • The reciprocal of the combined resistance is the sum of the reciprocals of the individual resistances
    
    Resistors connected in parallel
    
    Combined resistance of two or more resistors in parallel equation
  • This means the combined resistance decreases and is less than the resistance of any of the individual components
  • For example, If two resistors of equal resistance are connected in parallel, then the combined resistance will halve

Maths Tips

• The reciprocal of a value is 1 / value
• For example, the reciprocal of a whole number such as 2 equals ½
  • The reciprocal of ½ is 2
• If the number is already a fraction, the numerator and denominator are ‘flipped’ round
  
  The reciprocal of a number is 1 ÷ number
• In the case for the resistance R, this becomes 1/R. To get the value of R from 1/R, you must do 1 ÷ your answer
• You can also use the reciprocal button on your calculator (labelled either x-1 or 1/x, depending on your calculator
• The most common mistake is to forget to find 1/R_T and not RT . Remember to do 1 / answer to get this value

Question for Notes: Resistors in Parallel

Try yourself:The circuit below shows 3 resistors connected in parallel. 

Which value gives the combined resistance of all the resistors in this circuit? 

• A.

  5R/2
• B.

  2/5R
• C.

  5/2R
• D.

  2R/5

Explanation

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