Adding resistors in series
- Place several resistors one after the other on the same loop and their total resistance is found by adding the individual resistances together:
R_total = R₁ + R₂ + R₃ + …
- Adding another resistor in series makes the loop harder for charge to flow through, so the total current falls (for a fixed supply voltage)
- The total voltage from the supply is shared across the resistors in the same ratio as their resistances: a bigger resistor takes a bigger fraction of the voltage
Quick rules to recall
- For components in series:
- current is the same at every point in the loop
- the supply voltage is shared between components, in proportion to their resistances
- the total resistance is the sum of the individual resistances
- For components in parallel:
- the supply current splits between the branches and recombines at junctions
- every branch carries the full supply voltage
- the total resistance is less than the smallest individual branch resistance (a second branch always offers an extra path for charge, lowering overall resistance)
Calculating total resistance and current in a series circuit
A 9 V battery is connected in series with two resistors: one of 20 Ω and one of 25 Ω. Calculate the total resistance of the circuit and the current flowing through it.
Solution:
- Total resistance: R_total = R₁ + R₂ = 20 + 25 = 45 Ω
- Rearrange V = IR to give I = V / R
- I = 9 / 45 = 0.20 A