Series and Parallel Circuits

In a series circuit all components are on one single loop. Three rules:

1. Current — same at every point. $I_1 = I_2 = I_3 = \ldots$

2. Potential difference — the cell's p.d. is shared between components. $V_{\text{total}} = V_1 + V_2 + V_3 + \ldots$

3. Resistance — resistances add. $R_{\text{total}} = R_1 + R_2 + R_3 + \ldots$

Bigger total R means smaller current from the cell, by V = IR.

Worked example. A 12 V cell drives current through a 4 Ω and an 8 Ω resistor in series.

• Total R = 12 Ω.
• Current I = 12/12 = 1.0 A.
• p.d. across 4 Ω: V = 4 × 1 = 4 V.
• p.d. across 8 Ω: V = 8 × 1 = 8 V.
• Check: 4 + 8 = 12 V. ✓

In a parallel circuit there are branches that each provide an independent path.

1. Potential difference — the p.d. across each parallel branch is the SAME (equal to the cell's p.d.). $V_1 = V_2 = V_3 = \ldots = V_{\text{cell}}$

2. Current — the cell's current splits between branches; the branch currents add to give the total. $I_{\text{total}} = I_1 + I_2 + I_3 + \ldots$

3. Resistance — total R is LESS than the smallest individual R. (Why? Adding a branch provides extra current paths, so more current flows for the same p.d. → effective R falls.)

GCSE-level: you are NOT required to calculate parallel combined resistance using $1/R_T = 1/R_1 + 1/R_2$ — only to STATE that total R is less than the smallest.

Domestic UK wiring uses parallel for several reasons:

1. Every appliance gets the full 230 V mains voltage.
2. Appliances can be switched on/off independently.
3. If one bulb fails, others still work.
4. Adding extra appliances lowers total resistance — fuse and circuit breakers protect against overcurrent (covered in 4.2.3.2).

Old-fashioned Christmas tree lights used series — one dead bulb killed all the rest. Modern LED strings use parallel branches with intelligent control.