Series and parallel circuits

In a series circuit, the components are joined end to end in one loop.

• Current is the same through every component.
• The total pd from the supply is shared between the components.
• The total resistance is the sum of the resistances: R = R₁ + R₂

Example: a 2 Ω and a 4 Ω resistor are in series with a 12 V supply.

1. R = 2 + 4 = 6 Ω
2. I = V ÷ R = 12 ÷ 6 = 2 A through both
3. pd across 2 Ω = IR = 2 × 2 = 4 V
4. pd across 4 Ω = IR = 2 × 4 = 8 V

Check: 4 V + 8 V = 12 V, the supply pd.

In a parallel circuit, each component is on its own branch.

• The pd across each branch is the same as the supply pd.
• The total current is the sum of the currents in the branches.
• The total resistance is less than the smallest resistance on its own.

Example: a 6 Ω and a 3 Ω resistor are in parallel with a 6 V supply.

1. Current through 6 Ω: I = 6 ÷ 6 = 1 A
2. Current through 3 Ω: I = 6 ÷ 3 = 2 A
3. Total current = 1 + 2 = 3 A
4. Total resistance = 6 ÷ 3 = 2 Ω, less than 3 Ω

Adding a resistor in series makes the current pass through one more obstacle, so the total resistance goes up.

Adding a resistor in parallel gives the current an extra path. The pd across each branch stays the same, so the new branch carries its own current on top of the others. The supply now pushes more total current for the same pd, so the total resistance goes down.

Think of the checkouts in a shop: opening another till lets more people through at once, even if the new till is slow.