Parallel circuits · Year 12
In Year 12 you learn: parallel resistors: 1/R = 1/R₁ + 1/R₂.
In a parallel circuit there are branches. Each branch gets the full supply p.d., the branch currents add up to the total, and adding a branch lowers the total resistance. Homes are wired in parallel so each appliance works on its own.
Key facts
- Parallel resistors: 1/R = 1/(R₁) + 1/(R₂) + … (for two: product ÷ sum). The total is less than the smallest.
- Adding another resistor in parallel lowers the total resistance, because it adds another path for the current.
Worked examples
Example 1
A 12 V battery is connected to 4 Ω and 6 Ω resistors in parallel. Find the current through each resistor and the battery current.
Answer: 3 A and 2 A; 5 A from the battery
Example 2
Adding another resistor in parallel does what to the total resistance?
Answer: It goes down.
Example 3
Resistors of 10 Ω and 40 Ω are in parallel across 8 V. Which one carries more current, and how much more?
Answer: the 10 Ω resistor; 0.6 A more
Example 4
Find the combined resistance of 6 Ω and 3 Ω in parallel.
Answer: 2 Ω
Example 5
Resistors of 10 Ω, 20 Ω and 20 Ω are in parallel. Find the total resistance.
Answer: 5 Ω
Example 6
You need a combined resistance of 4 Ω but only have a 12 Ω resistor. What resistor must you connect in parallel with it?
Answer: 6 Ω