Series, parallel and electrical power

Series circuits

In a series circuit the components are connected one after another in a single loop, so the charge has only one path.

• Current is the same everywhere in the loop: I = I₁ = I₂.
• The voltages across the components add up to the supply voltage: V = V₁ + V₂. Each coulomb gives some of its energy to each component in turn. The bigger resistor gets the bigger share of the voltage.
• Resistances add: R = R₁ + R₂. Adding another component in series increases the total resistance, so the current falls.
• If one component breaks, the circuit is broken and everything stops (like old strings of Christmas lights).

Parallel circuits

In a parallel circuit each component is on its own branch, so the charge splits at a junction and rejoins afterwards.

• The voltage across each branch is the same as the supply: V = V₁ = V₂. Every coulomb gets the full energy, whichever branch it takes.
• The branch currents add up to the total current: I = I₁ + I₂. More current flows through the branch with less resistance.
• Adding a branch lowers the total resistance, because it opens another path. The total is always less than the smallest branch resistance. For two branches: 1/R = 1/R₁ + 1/R₂.
• Each branch can be switched on and off on its own, and if one breaks the others keep working. That's why houses are wired in parallel.

Electrical power

Power is the rate of transferring energy, measured in watts (W). One watt is one joule per second. Because voltage is energy per coulomb and current is coulombs per second, multiplying them gives energy per second:

power (W) = voltage (V) × current (A)
P = V I

The energy an appliance uses depends on its power and how long it runs. Electricity companies measure it in kilowatt-hours (kWh): the energy used by a 1000 W appliance running for one hour. 1 kWh = 3 600 000 J.

energy (kWh) = power (kW) × time (h)
cost = energy (kWh) × price per kWh

Household electricity in NSW typically costs around 30 to 40 cents per kWh in 2025–26 (it has risen a lot since the 20 cents often quoted in older textbooks). Rooftop solar owners are paid much less, often 5 cents or under, for electricity they export.

How a house is wired

• Electricity arrives at the switchboard, where the meter records the kWh used.
• Each circuit has a circuit breaker. If too much current flows (an overload or a short circuit), the wires would overheat and could start a fire, so the breaker switches off automatically. Older houses use fuses: thin wires that melt and break the circuit.
• The active wire (brown, or red in old houses) carries the 230 V supply. The neutral wire (blue, or black in old houses) completes the circuit. The earth wire (green and yellow) connects metal cases to the ground, so if a fault makes the case live, current flows safely to earth and trips the breaker.
• A safety switch (residual current device, RCD) compares the current in the active and neutral wires. If they differ by even 30 mA, some current must be leaking, perhaps through a person, and it cuts the power in about 30 milliseconds, fast enough to prevent a fatal shock. RCDs are required on new homes in Australia and have saved many lives. Press the test button every few months.

Electrical work in Australia must be done by a licensed electrician. Never use appliances near water, never poke anything into a power point, and stay at least 8 metres away from fallen power lines.