Series and parallel circuits (P3.3)
Gateway A loves a circuit-rules question with mid-circuit diagrams. Get the four rules in your head and you can answer almost anything.
Symbols you must know
| Symbol | Component |
|---|---|
| ──── | Wire / conductor |
| Two parallel lines (one short, one long) | Cell |
| ──[──] | Resistor |
| ──(L)── | Lamp |
| ──(A)── | Ammeter (placed in series, low resistance) |
| ──(V)── | Voltmeter (placed in parallel, high resistance) |
| Saw-tooth | Variable resistor |
| ⏞⏟ | Switch |
| (T) | Thermistor |
| (D) | LDR (light-dependent resistor) |
| → | Diode |
Series circuits — the four rules
In a series circuit, all components are on the same loop; current has only one path.
- Current is the same everywhere. I_total = I₁ = I₂ = I₃.
- Total p.d. = sum of p.d.s. V_total = V₁ + V₂ + V₃.
- Total resistance = sum of resistances. R_total = R₁ + R₂ + R₃.
- Adding more components in series increases total resistance → reduces current.
Parallel circuits — the four rules
In a parallel circuit, components are on separate branches; current has multiple paths.
- Total current = sum of branch currents. I_total = I₁ + I₂ + I₃.
- P.d. is the same across each branch. V_total = V₁ = V₂ = V₃.
- Total resistance is LESS than the smallest branch resistance. Adding more parallel branches decreases total resistance.
- Each branch operates independently — break one and the others still work. (This is why house wiring is parallel.)
Why parallel resistance decreases
Imagine a single resistor of 6 Ω. Now add another 6 Ω in parallel. You now have two paths for current — the total resistance is halved. Two paths = double the cross-sectional area = half the resistance.
For two equal resistors in parallel, R_total = R / 2.
Ohm's law (recap from P3.2)
V = I × R
Where V is potential difference (V), I is current A and R is resistance (Ω).
✦Worked example— Worked example — series
Three resistors of 4 Ω, 6 Ω and 10 Ω are in series with a 12 V cell.
- R_total = 4 + 6 + 10 = 20 Ω.
- I = V / R = 12 / 20 = 0.6 A (the same through every resistor).
- p.d. across 4 Ω = 0.6 × 4 = 2.4 V.
- p.d. across 6 Ω = 0.6 × 6 = 3.6 V.
- p.d. across 10 Ω = 0.6 × 10 = 6.0 V.
- Sum = 2.4 + 3.6 + 6.0 = 12 V ✓ (matches the cell).
✦Worked example— Worked example — parallel
Two 6 Ω resistors are in parallel with a 12 V cell.
- p.d. across each branch = 12 V.
- I in each branch = 12 / 6 = 2 A.
- Total current from cell = 2 + 2 = 4 A.
- Total resistance = V / I = 12 / 4 = 3 Ω.
- Note: 3 Ω is half of 6 Ω, as expected.
Mains wiring is parallel
Houses wire all sockets and lights in parallel because:
- Each appliance has the full mains p.d. across it (~230 V).
- One appliance failing or being switched off does not affect the others.
- Different appliances draw different currents independently.
Common Gateway-paper mistakes
- Adding parallel resistances directly (1/R rule for parallel — easier to remember "parallel = less than the smallest").
- Using V = IR with the wrong V (use the V across that specific component, not the cell e.m.f.).
- Forgetting that ammeters are placed in series and voltmeters in parallel.
- Drawing voltmeters in series — that breaks the circuit.
- Saying "current is used up" through a resistor — current is conserved, only energy is transferred.
➜Try this— Quick check
Two 4 Ω resistors are in parallel, connected to a 6 V cell.
- p.d. across each: 6 V.
- I in each branch: 6 / 4 = 1.5 A.
- Total current: 3 A.
- Total resistance: V / I = 6 / 3 = 2 Ω. ✓ (Half of 4 Ω.)
AI-generated · claude-opus-4-7 · v3-ocr-combined-science