17. Series and Parallel Circuits

Series circuits

In a series circuit, components are connected one after another in a single loop. There is only one path for the current.

Series: one loop, one path.

Rules for series circuits

Quantity	Rule
Current	The same everywhere: $I_{1} = I_{2} = I_{3}$
Voltage	Shared between components: $V_{total} = V_{1} + V_{2} + \dots$
Resistance	Adds up: $R_{total} = R_{1} + R_{2} + \dots$

What happens in real life

Adding more bulbs makes every bulb dimmer, because the voltage is shared and total resistance goes up.
If one bulb breaks, the loop is broken and all bulbs go out.

Parallel circuits

In a parallel circuit, components are on separate branches. The current splits up at a junction and joins again afterwards. There is more than one path.

Parallel: each lamp has its own branch. Dots mark the junctions.

Rules for parallel circuits

Quantity	Rule
Current	Splits between branches: $I_{total} = I_{1} + I_{2} + \dots$
Voltage	The same across every branch: $V_{1} = V_{2} = V_{supply}$
Resistance	Total is less than the smallest branch: $\frac{1}{R _{total}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \dots$

What happens in real life

Each bulb gets the full voltage, so they all stay bright.
If one bulb breaks, the others keep working.
Each branch can have its own switch.
This is how houses are wired. Your TV does not go off when someone turns off the kitchen light.

Series versus parallel at a glance

	Series	Parallel
Paths for current	One	More than one
Current	Same everywhere	Splits between branches
Voltage	Shared	Same on every branch
Adding bulbs	All get dimmer	Stay just as bright
One bulb breaks	All go out	Others stay on
Total resistance	Sum of all	Less than smallest

Circuits

Series

One loop
Same current
Voltage shared
R = R₁ + R₂
One breaks, all off

Parallel

Branches
Current splits
Same voltage
1/R = 1/R₁ + 1/R₂
House wiring

Checks

Voltages add to supply in series
Currents add to total in parallel

Quick summary

Series: one loop. Same current everywhere. Voltages add up. $R = R_{1} + R_{2}$ .
Parallel: branches. Same voltage on each branch. Currents add up. $\frac{1}{R} = \frac{1}{R _{1}} + \frac{1}{R _{2}}$ .
Series bulbs dim as you add more, and one break turns them all off.
Parallel bulbs stay bright and work independently. Homes use parallel wiring.
Parallel total resistance is always less than the smallest branch.

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