Compound DC Circuits
Introduced| English |
|---|
| series/ˈsɪəriːz/ |
| parallel circuit/ˈpærəlel ˈsɜːkɪt/ |
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 $\Omega$?
Series resistances add: $6 + 6 = 12\ \Omega$.
In a series circuit, the current through each component is:
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 $\Omega$?
$\tfrac1R = \tfrac16 + \tfrac16 = \tfrac26 \Rightarrow R = 3\ \Omega$.
Components in parallel all have the same ____ across them.
Parallel branches share the same two points, so the same voltage.
Select all true statements about series and parallel circuits.
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 smaller.
Each parallel branch is an extra path, lowering 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.