Electrical Power and Energy — Part 1: Power, energy and bills: visual lesson, ICSE Class 10 Physics (Science Paper 1)

Lesson

Where do the units on the bill come from?

Part 1 — every appliance converts electrical energy at its own rate. The bill counts that energy in units (kilowatt hours).

In this lesson you will

Derive and use W = VIt = I²Rt = V²t/R and P = VI = I²R = V²/R
Interpret a power rating such as 1000 W, 220 V
Use the kilowatt hour and calculate the cost of electricity for a household

Table of four household appliances, their ratings and the form of energy they produce
Appliance	Typical rating	Energy goes to
LED tube light	20 W, 220 V	Light (and a little heat)
Ceiling fan	75 W, 220 V	Motion
Electric iron	1000 W, 220 V	Heat
Geyser	2000 W, 220 V	Heat

Concept

Electrical energy

When a charge Q moves through a p.d. V, the work done is $W = QV$ . Since $Q = It$ , $W = VIt$ . Using $V = IR$ : $W = I^{2}Rt$ ; using $I = V/R$ : $W = \dfrac{V^{2}t}{R}$ . In a resistor all this energy becomes heat (Joule’s law of heating: $H = I^{2}Rt$ ). SI unit: joule.

Concept

Electrical power

Electrical power is the rate at which electrical energy is converted: $P = \dfrac{W}{t} = VI = I^{2}R = \dfrac{V^{2}}{R}$ . SI unit watt (W): 1 W = 1 J s⁻¹; 1 kW = 1000 W. Use $P = I^{2}R$ when the current is common (series), and $P = \dfrac{V^{2}}{R}$ when the voltage is common (parallel, mains).

Table of the three power formulae with an example of each
Formula	Best when you know	Example
P = VI	V and I	220 V, 5 A: 1100 W
P = I²R	I and R	2 A in 50 Ω: 200 W
P = V²/R	V and R	220 V across 110 Ω: 440 W

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