Series and Parallel Circuits

Series circuit — components connected one after another in a single loop, so there is only one path for the current.

In series:

• The current is the same everywhere in the loop.
• The p.d.s add up to the supply voltage: V total = V₁ + V₂ + V₃
• The resistances add: R total = R₁ + R₂ + R₃
• Break the circuit anywhere and everything stops.

Parallel circuit — components connected across the same two points, so the current has more than one path.

In parallel:

• The p.d. is the same across each branch, and equal to the supply.
• The currents in the branches add to the total: I total = I₁ + I₂ + I₃
• The total resistance is less than the smallest individual resistance, because adding a branch gives the current another route.
• One branch can be switched off or fail without affecting the others.

Why house lighting is wired in parallel. Every lamp gets the full mains voltage, each has its own switch, and one blown bulb leaves the rest working. In series they would share the voltage, all be dim, and all go out together.

Adding a resistor in parallel lowers the total resistance. This surprises people, since adding something ought to add resistance. It helps to think of doors out of a room: a second door lets more people leave per second, however narrow it is.

Current at a junction — the current entering a junction equals the current leaving it. Charge is not created or lost at a branch.

Example: a 6 V supply with a 4 Ω and a 2 Ω resistor in series has a total resistance of 6 Ω, so the current is 1 A throughout, and the p.d.s are 4 V and 2 V, which add to the supply. Put the same two in parallel and each has the full 6 V across it, drawing 1.5 A and 3 A, a total of 4.5 A — so the combined resistance is 6 ÷ 4.5 = 1.3 Ω, less than either resistor alone.