Parallel circuits · Grade 11

In Grade 11 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: each branch has the full supply p.d.; currents add: I = I₁ + I₂ + …
  • 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

Two lamps are in parallel with a 6 V battery. What is the p.d. across each lamp?

Answer: 6 V

Example 2

Two identical lamps are in parallel. The ammeter next to the battery reads 1.5 A. What current flows through each lamp?

Answer: 0.75 A

Example 3

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 4

Adding another resistor in parallel does what to the total resistance?

Answer: It goes down.

Example 5

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 6

Find the combined resistance of 6 Ω and 3 Ω in parallel.

Answer: 2 Ω

Example 7

Resistors of 10 Ω, 20 Ω and 20 Ω are in parallel. Find the total resistance.

Answer: 5 Ω

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