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
Example — three resistors of 25 Ω, R₂ and 15 Ω are wired in series with a battery. A voltmeter across the whole combination reads 80 V and an ammeter in the loop reads 1.0 A. Find R₂.
- The total resistance from V = I × R is R_total = 80 / 1.0 = 80 Ω
- Series totals add: 80 = 25 + R₂ + 15
- R₂ = 80 − 25 − 15 = 40 Ω
Example — a 1.5 A current flows through a 6.0 Ω fixed resistor in a series circuit. Calculate the voltage across the resistor.
- Apply V = I × R: V = 1.5 × 6.0 = 9.0 V
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)