Split or Stack

Why it matters

One bulb blows in your fairy lights and ALL of them die. A bulb blows at home and nothing else even blinks. Same electricity — different wiring.

The idea in plain words

Two combination rules run every circuit in the world. Tap the terms.

Rs = R₁ + R₂ · 1/Rp = 1/R₁ + 1/R₂

R₁ = 4 Ω and R₂ = 8 Ω. Combine them both ways.

Rp = 8/3 ≈ 2.67 Ω — smaller than either branch!

• ohm (Ω): Rs — series total — resistances stack, always BIGGER than each part
• ohm (Ω): Rp — parallel total — always SMALLER than the smallest branch
• ohm (Ω): R₁ — first resistor (our 4 Ω bulb)
• ohm (Ω): R₂ — second resistor (our 8 Ω bulb)
• Series: Rs = 4 + 8 = 12 Ω
• Parallel: 1/Rp = 1/4 + 1/8 = 3/8

Predict first

Two bulbs glow in series. Compared to the ammeter BEFORE the first bulb, the ammeter AFTER the second bulb reads…

Charge is never used up. The SAME current threads every point of a series loop — what the bulbs take is energy, not current.

• exactly the same — correct
• less — the bulbs use up some current
• more

What you do

Run the series loop, then the parallel one. In each, tap the ammeter you think reads the MOST current — the meters will settle the argument.

Check yourself

Why are the appliances in your house wired in parallel?

In parallel every branch sees the full supply and can be switched independently — one failure doesn't darken the house.

Three 3 Ω resistors in parallel give…

1/Rp = 1/3 + 1/3 + 1/3 = 1 → Rp = 1 Ω. More parallel paths, easier flow.

In a SERIES pair, which bulb glows brighter?

Series means the same I everywhere, so P = I²R — the bigger R converts more power. (In parallel it flips: P = V²/R.)

• Each gets the full mains voltage and its own switch — correct
• Parallel wiring uses less current
• It is cheaper to wire
• 1 Ω — correct
• 9 Ω
• 3 Ω
• The one with more resistance — correct
• The one with less resistance
• Both equally, always