Jupiter2U School
Chapter 15

Electricity & Circuits

High School
At a glance
Core ideaCurrent is flowing charge; Ohm's law V = IR ties voltage, current and resistance together.
Key termResistance — opposition to current; it adds in series, divides in parallel.
You can…Reduce a series-parallel network and find its currents and power.
Watch outIt's current, not voltage alone, that harms; a bird on one wire has no potential difference across it.
Theory

Charge, current and Ohm's law

Electric charge Q (coulombs) comes in multiples of e = 1.602×10⁻¹⁹ C. Current is the rate of flow of charge:

I = Q / t amperes, A = C·s⁻¹

Potential difference (voltage) V is energy per unit charge, V = W/Q (volts, J·C⁻¹). Resistance opposes current; Ohm's law for ohmic conductors:

V = IR R in ohms, Ω

Combining resistors and power

Series: R = R₁ + R₂ + … (same current, voltages add). Parallel: 1/R = 1/R₁ + 1/R₂ + … (same voltage, currents add). Electrical power dissipated:

P = VI = I²R = V²/R watts

Kirchhoff's laws: charge conservation — currents into a junction sum to zero; energy conservation — voltages around any loop sum to zero.

12V 4Ω 6Ω 3Ω
A 4Ω resistor in series with a parallel pair (6Ω and 3Ω) — series resistances add, parallel branches share current.
Explanation

Water pipes and why birds don't fry

A helpful analogy: voltage is like pressure, current like flow rate, and resistance like a narrow pipe. A battery is a pump maintaining pressure. This intuition correctly predicts that adding resistors in series (more narrow pipe) reduces current, while parallel paths (extra pipes) increase total flow.

Series circuit

  • One single loop — same current everywhere
  • Voltages add: V = V₁ + V₂ + …
  • Resistances add: R = R₁ + R₂ + …
  • One break stops the whole circuit (old fairy lights)

Parallel circuit

  • Multiple branches — same voltage across each
  • Currents add: I = I₁ + I₂ + …
  • 1/R = 1/R₁ + 1/R₂ + … (total less than smallest)
  • Each branch works independently (house wiring)

Why can a bird sit safely on a high-voltage wire? Current needs a potential difference across the object. Both the bird's feet touch the same wire at nearly the same potential — almost no voltage across it, so almost no current. Danger arises only if it also touched the ground or another wire, completing a circuit across a large voltage.

It's current that kills. As little as ~100 mA through the heart can be fatal. High voltage is dangerous because it can drive large current through the body's resistance (I = V/R) — but a stun from static at thousands of volts carries negligible charge and energy.
Practical

Worked example — a series-parallel network

A 12 V battery connects to a 4 Ω resistor in series with a parallel pair of 6 Ω and 3 Ω. Find the total current and the power in the 4 Ω resistor.

  1. Parallel combination: 1/Rp = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, so Rp = 2 Ω.
  2. Total resistance: R = 4 + 2 = 6 Ω.
  3. Total current from battery: I = V/R = 12/6 = 2.0 A.
  4. Power in the 4 Ω resistor: P = I²R = 2.0² × 4 = 16 W.
  5. Check the parallel branch: it drops Vp = I·Rp = 2.0×2 = 4 V; currents 4/6 = 0.67 A and 4/3 = 1.33 A sum to 2.0 A. ✓

The full circuit uses P = VI = 12×2.0 = 24 W: 16 W in the series resistor, 8 W shared in the parallel pair.

Q&A
Why are house lights wired in parallel, not series?

In parallel each bulb gets the full mains voltage and works independently — switch one off (or let it fail) and the others stay lit. In series, all share the voltage and one broken bulb breaks the whole circuit (the old fairy-light problem).

A 2 kW kettle runs on 230 V mains. What current does it draw, and what fuse is appropriate?

I = P/V = 2000/230 = 8.7 A. A 13 A fuse is standard and appropriate — above the working current but able to blow on a genuine fault. A 5 A fuse would blow immediately; a 30 A fuse would fail to protect.

Two 10 Ω resistors: what total resistance in series versus parallel?

Series: 10 + 10 = 20 Ω. Parallel: 1/R = 1/10 + 1/10 = 2/10, so R = 5 Ω. Identical resistors in parallel give half the value; the total is always less than the smallest branch.

How does a fuse protect a circuit?

A fuse is a thin wire that heats by I²R. If current exceeds its rating (e.g. a short circuit), the wire melts and breaks the circuit, cutting the current before wiring overheats and causes a fire. It is a deliberate weak link.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Charge & currentOhm's lawResistanceSeriesParallelPower P=V*IElectricity & Circuits
Infographic

The key facts, visualised

V = I*R
Ohm's law relates voltage, current, resistance
I = Q/t
Current is charge flow per second, in amps
P = V*I
Electrical power in watts
Series adds R
Parallel adds 1/R for resistors
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1A 12 V battery drives 3.0 A through a resistor. Find its resistance.

  1. V = I*R so R = V/I
  2. R = 12 / 3.0

Example 2Two resistors, 3 ohm and 6 ohm, are in parallel. Find the total resistance.

  1. 1/R = 1/3 + 1/6 = 2/6 + 1/6 = 3/6
  2. 1/R = 1/2
  3. R = 2 ohms
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1Find the current when 9 V is across a 3 ohm resistor.
I = V/R = 9/3 = 3 A.
2Two 4 ohm resistors in series: total resistance?
4 + 4 = 8 ohms.
3A 60 W bulb runs at 120 V. Find its current.
I = P/V = 60/120 = 0.5 A.
4Why do birds on a single wire not get shocked?
Both feet are at nearly the same voltage, so almost no current flows through the bird.
5How does current split at a parallel junction?
It divides among the branches, more through the lower resistance path.
6What is the charge if 2 A flows for 10 s?
Q = I*t = 2*10 = 20 C.