Electric Circuits · Grade 10
Why do the other lights stay on when one bulb blows at home?
Because a house is wired in parallel. In a series circuit there is only one path, and a blown bulb breaks it for everything. In parallel each bulb has its own branch, so one going out does not touch the rest. It is also why every socket in the house receives the full voltage.
Learning objectives
- Calculate the equivalent resistance of resistors in series and of resistors in parallel
- Explain why the equivalent resistance of a parallel combination is smaller than any single resistor in it
- Predict what happens to the remaining lamps when one lamp burns out, in a series circuit and in a parallel circuit
- Find the current in every branch of a circuit that mixes series and parallel sections
Two ways to connect
In series the components sit in a single chain. The same current passes through all of them, and the voltage divides between them.
In parallel each component has its own branch between the same two points. The same voltage is across all of them, and the current divides between the branches.
That inversion is the whole difference, and it is worth remembering as a pair: in series the current is shared and the voltage divides; in parallel the voltage is shared and the current divides.
Equivalent resistance
In series you simply add: the equivalent resistance is the sum. Adding a resistor always increases the total.
In parallel you add the reciprocals: one over the equivalent equals the sum of one over each resistor. For two resistors there is a convenient shortcut — the product over the sum.
The parallel result is always smaller than any single resistor in it, which sounds wrong until you think in terms of paths: every extra branch is another route opened, and another route always makes the journey easier.
Why houses are wired in parallel
If a house were wired in series, every appliance would get only a share of the voltage, and switching on one more would weaken all the others. A blown bulb would darken the house.
In parallel every appliance receives the full voltage, each can be switched on and off independently, and a fault in one does not touch the rest.
The price is that every extra appliance lowers the total resistance and raises the overall current — which is why a house has a fuse or a breaker, the subject of the last lesson.
Worked examples
Resistors of 3 and 6 ohms in series. What is the equivalent resistance?
- In series you add
- 3 plus 6
Answer: 9 ohms
The same resistors in parallel. What is the equivalent resistance?
- For two resistors: product over sum
- 3 times 6 is 18
- 3 plus 6 is 9
Answer: 2 ohms — smaller than either of them
Three identical lamps in parallel across a battery. One blows. What happens to the other two?
- Each lamp has its own branch
- The voltage across each branch is the battery's
- Breaking one branch does not change the others
Answer: They carry on at the same brightness
Common mistakes
- Adding parallel resistances as if they were in series
- In parallel you add the reciprocals. A plain sum gives a result larger than either resistor, while the correct answer is smaller than both.
- Thinking the current is shared in parallel
- In parallel the voltage is shared and the current divides. In series it is exactly the other way round, and swapping the two causes most errors in this topic.
- Assuming another appliance lowers the voltage
- In parallel every appliance gets the full voltage. What rises is the total current, and that is what the fuse is watching.
What to remember
- Series: shared current, divided voltage, resistances add.
- Parallel: shared voltage, divided current, reciprocals add.
- A parallel combination is always smaller than any resistor in it.
- Houses are wired in parallel so one fault cannot darken everything.