Resistors in Series

When two or more resistors are connected in series, the total resistance is equal to the sum of their individual resistances
For two resistors of resistance R₁ and R₂, the total resistance can be calculated using the equation:

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

Where:
- R is the total resistance, in ohms (Ω)

Increasing the number of resistors increases the overall resistance
- The charge now has more resistors to pass through

The total voltage is also the sum of the voltages across each of the individual resistors

combined-resistance, IGCSE & GCSE Physics revision notes

Three resistors connected in series. The total voltage is the sum of the individual voltages, and the total resistance is the sum of the three individual resistances

Summary of series and parallel circuits

For components connected in series:
- the current is the same at all points and in each component
- the voltage of the power supply is shared between the components
- the total resistance is the sum of the resistances of each component

For components connected in parallel:
- the current from the supply splits in the branches
- the voltage across each branch is the same
- the total resistance is less than that of each component

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: Write down the equation for the combined resistance in series

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

Step 2: Substitute the values for total resistance R and the other resistors

60 Ω = 30 Ω + R₂ + 10 Ω

Step 3: Rearrange for R₂

R₂ = 60 Ω – 30 Ω – 10 Ω = 20 Ω

Worked example

Dennis sets up a series circuit as shown below.

WE Series Circuit Question image, downloadable IGCSE & GCSE Physics revision notes

The cell supplies a current of 2 A to the circuit, and the fixed resistor has a resistance of 4 Ω.

(a) How much current flows through the fixed resistor?

(b) What is the reading on the voltmeter?

Answer:

Part (a)

Step 1: Recall that current is conserved in a series circuit

Since current is conserved in a series circuit, it is the same size if measured anywhere in the series loop
This means that since the cell supplies 2 A to the circuit, the current is 2 A everywhere
Therefore, 2 A flows through the fixed resistor

Part (b)

Step 1: List the known quantities

Current, I = 2 A
Resistance, R = 4 Ω

Step 2: State the equation linking potential difference, resistance and current

The equation linking potential difference, resistance and current is:

$V = I \times R$

Step 3: Substitute the known values into the equation and calculate the potential difference

V = 2 × 4 = 8 V

Therefore, the voltmeter reads 8 V across the fixed resistor

Resistors in Series (Edexcel IGCSE Physics: Double Science)

Revision Note