Parallel circuits · Grade 12

In Grade 12 you get fluent with: current in each parallel branch; 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

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