SPI Physics · Electricity and Magnetism

Electric Power and House Wiring

Electric power is the energy used each second, P = VI; energy is power times time, billed in kilowatt hours; and a house circuit is kept safe by a fuse, a main switch and an earth wire.

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Why this matters

Eight questions in the bank, seven EASY and one MODERATE. Five are about power and energy (P = VI, a halved voltage, a bulb's energy in a minute, the kWh unit, why LEDs are preferred) and three are house wiring: the fuse, what a fuse wire must be, and what the main switch cuts. Units cost most of the marks: milliamperes, minutes and watt hours.

Concept 1 of 3: Electric power: P = VI

Power is how fast an appliance uses energy. A 1000 W heater uses energy ten times as fast as a 100 W bulb. Multiply the voltage by the current and you get the power.

Definition

$P = VI$ . Unit: watt (W); $1\text{ kW} = 1000\text{ W}$ .
With Ohm's law it also reads $P = I^2R$ and $P = \dfrac{V^2}{R}$ .
For a fixed resistor, power goes as the square of the voltage (or of the current): halve V and P becomes one fourth; double I and P becomes four times.
A rating like '100 W, 220 V' gives the resistance: $R = \dfrac{V^2}{P} = \dfrac{220^2}{100} = 484\,\Omega$ .
An LED turns much more of its energy into light and much less into heat than a filament bulb, so it gives the same light for far less power.

Electric power

P = VI = I^2R = \frac{V^2}{R}

Worked example

A heater draws a current of 4 A from a 230 V supply. Find its power.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 1 · Electricity and Magnetism · Electric Power and House Wiring

An electric bulb is connected to a power supply of 220 V. If the current drawn by the bulb from the supply is 500 mA, the power of the bulb is:

Halving the voltage halves the power

For a fixed resistor

P = \frac{V^2}{R}

, so halving V gives one fourth of the power, not half.

Using milliamperes as amperes

Change mA to A before multiplying: 300 mA is 0.3 A, so at 220 V the power is 66 W, not 66000 W.

Drill 2 more on electric power: p = vi

Concept 2 of 3: Electrical energy and the kilowatt hour

Energy is power kept up for a time. A bulb's power tells you how fast it uses energy; leave it on longer and it uses more. The electricity bill counts energy in large units called kilowatt hours.

Definition

$E = Pt$ . With P in watts and t in seconds, E is in joules.
With P in kilowatts and t in hours, E is in kilowatt hours (kWh). One kWh is one unit on the bill.
With P in watts and t in hours: $E = \dfrac{Pt}{1000}$ kWh.
$1\text{ kWh} = 1000\text{ W} \times 3600\text{ s} = 3.6 \times 10^6\text{ J}$ .
The kWh is a unit of energy, not of power.

Electrical energy

E = Pt \qquad E\,(\text{kWh}) = \frac{P\,(\text{W}) \times t\,(\text{h})}{1000} \qquad 1\text{ kWh} = 3.6 \times 10^6\text{ J}

Worked example

A 1500 W heater runs for 2 hours. How many units of electricity does it use?

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 2 · Electricity and Magnetism · Electric Power and House Wiring

How much energy is does a 100W electric bulb transfer in 1 minute?

Leaving time in minutes

In joules the time must be in seconds. A 50 W lamp for 3 minutes uses

50 \times 180 = 9000

J, not 150 J.

Calling the kWh a unit of power

Kilowatt is power; kilowatt HOUR is energy. The bill counts kWh because it charges for energy used.

Drill 1 more on electrical energy and the kilowatt hour

Concept 3 of 3: House wiring and safety devices

Mains electricity in India comes into a house on two wires at 220 V, 50 Hz, with a third wire for safety. Each safety device guards against one danger, and the questions ask which device does which job.

Definition

Three rules settle most questions:

The fuse and every switch go in the live wire, in series with the appliance.
The fuse protects the circuit and appliances from overloading and short circuits; earthing protects people from shocks.
A fuse wire must melt quickly: it is thin, short, of low melting point and of higher resistance than the rest of the wiring.

Part	What it is or does
Live wire	Red insulation, at 220 V
Neutral wire	Black insulation, at zero potential
Earth wire	Green insulation, joined to the metal body of an appliance and to a plate buried in the ground
Fuse	A wire that melts and breaks the circuit when too much current flows
MCB (miniature circuit breaker)	A switch that trips by itself on too much current, and can be reset
Main switch	A double pole switch that cuts both the live and the neutral wire The earth wire is never switched off.
Short circuit	Live and neutral touch, so the resistance drops and a huge current flows
Overloading	Too many appliances on one socket draw more current than the wiring is meant for

Indian mains: 220 V AC at 50 Hz. Appliances are joined in parallel.

Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionEasy

Example 3 · Electricity and Magnetism · Electric Power and House Wiring

The most important safety device method used for protecting electrical appliances from short circuiting or overloading is

A thick fuse wire

A thick wire has low resistance and does not melt easily, so it fails to break the circuit. A fuse wire is thin.

Earthing as protection against overload

Earthing carries a leaking current away from a metal body to save the user. Overload and short circuit are the fuse's job.

Drill 2 more on house wiring and safety devices

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Electric power: P = VI
Electric power
$P = VI = I^2R = \frac{V^2}{R}$
Electrical energy and the kilowatt hour
Electrical energy
$E = Pt \qquad E\,(\text{kWh}) = \frac{P\,(\text{W}) \times t\,(\text{h})}{1000} \qquad 1\text{ kWh} = 3.6 \times 10^6\text{ J}$

Reference tables (1)

House wiring and safety devices8 rows

Part	What it is or does
Live wire	Red insulation, at 220 V
Neutral wire	Black insulation, at zero potential
Earth wire	Green insulation, joined to the metal body of an appliance and to a plate buried in the ground
Fuse	A wire that melts and breaks the circuit when too much current flows
MCB (miniature circuit breaker)	A switch that trips by itself on too much current, and can be reset
Main switch	A double pole switch that cuts both the live and the neutral wire The earth wire is never switched off.
Short circuit	Live and neutral touch, so the resistance drops and a huge current flows
Overloading	Too many appliances on one socket draw more current than the wiring is meant for

Indian mains: 220 V AC at 50 Hz. Appliances are joined in parallel.

Watch out for (6)

Halving the voltage halves the power
→ Electric power: P = VI
Using milliamperes as amperes
→ Electric power: P = VI
Leaving time in minutes
→ Electrical energy and the kilowatt hour
Calling the kWh a unit of power
→ Electrical energy and the kilowatt hour
A thick fuse wire
→ House wiring and safety devices
Earthing as protection against overload
→ House wiring and safety devices

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