Compound DC Circuits
Introduced| English | Meaning |
|---|---|
| series/ˈsɪəriːz/ | An arrangement in which components lie along a single electrical path. |
| parallel circuit/ˈpærəlel ˈsɜːkɪt/ | parallel circuit |
Fairy lights: one dead bulb, and the whole string goes out
- Old fairy lights were wired in a single line — one broken bulb killed them all.
- Modern ones keep glowing because they are wired a different way.
- The two ways to connect components are series 串联 and parallel circuit 并联.
- Which you choose changes the total resistance, the current, and what happens when one fails.
Series: one single path
- In series, components sit in a single line, one after another.
- The same current flows through each, and the voltages add up to the supply voltage.
- Resistances add: $R_{\text{total}} = R_1 + R_2 + \cdots$.
- Break any one and the whole loop stops — like the old fairy lights.
Two $6\ \Omega$ resistors are in series. What is the total resistance, in $\Omega$?
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Series resistances add: $6 + 6 = 12\ \Omega$.
In a series circuit, the current through each component is:
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One path means the same current flows through every series component.
Parallel: separate branches
- In parallel, components sit on separate branches across the same two points.
- Each branch has the same voltage, and the branch currents add to the total.
- The total resistance is less than any single branch: $\dfrac{1}{R_{\text{total}}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \cdots$.
- Break one branch and the others keep working — like modern lights and home wiring.
Series vs parallel
Switch between series and parallel and see how the current through each bulb changes.
Two $6\ \Omega$ resistors are in parallel. What is the total resistance, in $\Omega$?
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$\tfrac1R = \tfrac16 + \tfrac16 = \tfrac26 \Rightarrow R = 3\ \Omega$.
Components in parallel all have the same ____ across them.
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Parallel branches share the same two points, so the same voltage.
Select all true statements about series and parallel circuits.
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Series add; parallel give a smaller total; homes use parallel. Parallel resistances do not simply add.
Why homes wire in parallel
- Household sockets are all in parallel, so each gets the full mains voltage.
- You can switch one appliance off without cutting power to the rest.
- Adding more parallel paths lowers the total resistance and draws more total current.
- That is why overloading a circuit (too many devices) can trip a breaker.
Adding a resistor in parallel makes the total resistance larger.
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False. Each parallel branch is an extra path for current, so adding one lowers the total resistance.
Adding resistors in parallel makes the total resistance smaller, not larger — a surprise for many students. Each new branch is an extra path for current, so more current flows overall even though you "added a resistor".
Two $6\ \Omega$ resistors are connected (a) in series, (b) in parallel. Find each total.
- Series: $R = 6 + 6 = 12\ \Omega$.
- Parallel: $\dfrac{1}{R} = \dfrac{1}{6} + \dfrac{1}{6} = \dfrac{2}{6}$, so $R = 3\ \Omega$.
Series components share one path: currents equal, voltages add, resistances add ($R = R_1+R_2$). Parallel components share two points: voltages equal, currents add, and the total resistance is smaller than any branch ($\tfrac1R = \tfrac1{R_1}+\tfrac1{R_2}$). Homes wire in parallel.
Write from series 20 ohm and parallel 5 ohm
- Two resistors are each 10 ohm.
- Find the total in series, then the total in parallel.
Two resistors of 10 ohm each are connected first in series and then, separately, in parallel. What is the total resistance in each arrangement, in ohms?
Series adds. Two equal parallel resistors give half of one.
What is the parallel total of the two 10 ohm resistors?
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Two equal resistors in parallel have half the resistance of one. Other options — 20 ohm (the series total); 3 ohm (the lesson parallel total).