Series and Parallel Circuits (P2.2)

Series circuits

All components connected in a single loop.

Rules:

• Current is the same at all points: I₁ = I₂ = I₃ = I (amps don't "pile up")
• Voltage adds up: V_total = V₁ + V₂ + V₃
• Resistance adds up: R_total = R₁ + R₂ + R₃

If one component fails (opens circuit) — all components stop working.

Parallel circuits

Components connected on separate branches.

Rules:

• Voltage is the same across each branch: V₁ = V₂ = V₃ = V_supply
• Current splits and adds up: I_total = I₁ + I₂ + I₃
• Total resistance is LESS than smallest individual resistor:
  1/R_total = 1/R₁ + 1/R₂ + 1/R₃

If one component fails — others continue working (why houses use parallel circuits).

Calculations in series

Example: 12 Ω and 8 Ω in series, connected to 20 V battery.
R_total = 12 + 8 = 20 Ω
I = V/R = 20/20 = 1 A through each resistor
V across 12 Ω: V = IR = 1 × 12 = 12 V
V across 8 Ω: V = 1 × 8 = 8 V ✓ (12 + 8 = 20 V)

Calculations in parallel

Example: 6 Ω and 12 Ω in parallel, 12 V supply.
V across each = 12 V
I through 6 Ω: I = 12/6 = 2 A
I through 12 Ω: I = 12/12 = 1 A
I_total = 2 + 1 = 3 A
1/R_total = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 → R_total = 4 Ω

Measuring with meters

• Ammeter: connected in series (must be in the main current path); low resistance.
• Voltmeter: connected in parallel across a component; very high resistance (doesn't divert current).

Common exam errors

1. Saying current in a series circuit decreases after each resistor — current is the same throughout.
2. Mixing up series and parallel resistance formulas.
3. Forgetting that in parallel circuits, the total resistance is LESS than the smallest individual resistor.