S2 Science · Chapter 13
Electrical Circuits
Series & Parallel — interactive notes by The Classroom
What is a series circuit?
All components are connected in a single loop — there is only one path for current to flow. If one component breaks, the whole circuit stops working.
Current
I₁ = I₂ = I₃
Same everywhere
Voltage
V = V₁ + V₂
Voltages add up
Resistance
Rₜ = R₁ + R₂
Gets bigger
💡 Memory trick: Series = one lane road. Current can't split, so it stays the same throughout. All components share the same loop.
Try it — adjust the values
Total resistance Rₜ6 Ω
Current I (= V ÷ Rₜ)2.00 A
Voltage across R₁8.00 V
Voltage across R₂4.00 V
What is a parallel circuit?
Components are connected across the same two points — current has multiple paths to choose from. If one branch breaks, current keeps flowing through the others.
Current
I₁ = I₂ + I₃
Splits at junction
Voltage
V = V₁ = V₂
Same across each branch
Resistance
1/Rₜ = 1/R₁ + 1/R₂
Gets smaller
💡 Memory trick: Parallel = multiple lanes on a highway. Current splits and takes different routes. More lanes = less overall resistance.
Why does resistance decrease in parallel?
Adding more branches gives current more paths — it becomes easier for current to flow overall. Think of opening a second checkout lane at NTUC.
Shortcut formula: Rₜ = (R₁ × R₂) ÷ (R₁ + R₂)
Try it — adjust the values
Effective resistance Rₜ1.33 Ω
Total current I₁9.00 A
Current through R₁ (I₂)6.00 A
Current through R₂ (I₃)3.00 A
Voltage across each branch12 V
Series vs Parallel — side by side
| Property | Series | Parallel |
|---|---|---|
| Current paths | One path only | Multiple paths |
| Current rule | Same: I₁ = I₂ = I₃ | Splits: I₁ = I₂ + I₃ |
| Voltage rule | Adds up: V = V₁ + V₂ | Same: V = V₁ = V₂ |
| Resistance | Rₜ = R₁ + R₂ (↑ bigger) | 1/Rₜ = 1/R₁ + 1/R₂ (↓ smaller) |
| If one breaks | Whole circuit stops | Others still work |
| Real-life | Old fairy lights | Lights in your home |
🏠 Your home uses parallel circuits — each power socket gets the same voltage (230V). If one light blows, the rest stay on.
Q1 — Series circuit
A 4V battery is connected in series with a 1 Ω and 3 Ω resistor.
(a) Total resistance (Ω):
(b) Current from battery (A):
(c) Voltage across the 3 Ω (V):
Q2 — Parallel circuit
A 2 Ω and 4 Ω resistor are connected in parallel across a 2V battery.
(a) Effective resistance (Ω, 2 d.p.):
(b) Current through 2 Ω (A):
(c) Current through 4 Ω (A):
(d) Total current from battery (A):