Resistors in Series (Cambridge International AS Physics)

Deriving the Equation for Resistors in Series

• In a series circuit, the combined resistance of two or more resistors is the sum of the individual resistances

• In a series circuit:

  • The current is the same through all resistors
  • The potential difference is shared between all the resistors

• The equation for combined resistors in series is derived using Kirchhoff’s laws:

Resistors in Series

• When two or more components are connected in series: The combined resistance of the components is equal to the sum of the individual resistances

Resistors in series

Resistors connected in series each have their own separate potential difference

• The equation for the combined resistance, R of resistors in series is:

$R=R_{1}+R_{2}+...$

Worked Example The combined resistance R in the following series circuit is 60 Ω.

What is the resistance value of R₂?

A. 100 Ω

B. 30 Ω

C. 20 Ω

D. 40 Ω

Answer: C

Step 1: State the equation for the combined resistance for resistors in series

$R=R_{1}+R_{2}+...=R_{1}+R_{2}+R_{3}$

Step 2: Rearrange for resistance R₂

$R_{2} = R - ( R_{1} + R_{3} )$

Step 3: Substitute the values

R _ 2 = 60 - ( 30 + 10 ) = 20 capital omega