Parallel circuits · Grade 10
In Grade 10 you learn: 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.
- If one bulb breaks in parallel, only its branch stops: the others stay on.
- Adding another resistor in parallel lowers the total resistance, because it adds another path for the current.
Worked examples
Example 1
The ammeters in the branches read 0.4 A and 0.7 A. What does the ammeter by the battery read?
Answer: 1.1 A
Example 2
In a parallel circuit the ammeter next to the cell reads 0.9 A. The ammeter in one branch reads 0.5 A. What does the ammeter in the other branch read?
Answer: 0.4 A
Example 3
One bulb breaks in a parallel circuit of three bulbs. What happens to the other two?
Answer: They stay on.
Example 4
Why are the lights and sockets in a house wired in parallel?
Answer: Each one gets the full mains p.d. and can be switched on and off on its own.
Example 5
Two lamps are in parallel with a 6 V battery. What is the p.d. across each lamp?
Answer: 6 V
Example 6
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 7
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 8
Adding another resistor in parallel does what to the total resistance?
Answer: It goes down.
Example 9
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 10
Find the combined resistance of 6 Ω and 3 Ω in parallel.
Answer: 2 Ω
Example 11
Resistors of 10 Ω, 20 Ω and 20 Ω are in parallel. Find the total resistance.
Answer: 5 Ω