Electrical Power, Energy and Household Circuits notes: ICSE Class 10 Physics (Science Paper 1)

1. Electrical energy and power

Energy: $W = QV = VIt = I^{2}Rt = \dfrac{V^{2}t}{R}$ (joule). In a resistor it all becomes heat (Joule heating).
Power: $P = \dfrac{W}{t} = VI = I^{2}R = \dfrac{V^{2}}{R}$ (watt; 1 W = 1 J s⁻¹; 1 kW = 1000 W; 1 MW = 10⁶ W).
Use $I^{2}R$ when the current is common (series) and $V^{2}/R$ when the voltage is common (parallel, mains).

Table of which power formula to use for each pair of known quantities
Known	Use
V and I	P = VI
I and R	P = I²R
V and R	P = V²/R

Formulas

Electrical energy
$W = VIt = I^{2}Rt = \dfrac{V^{2}t}{R}$
Electrical power
$P = VI = I^{2}R = \dfrac{V^{2}}{R}$

Key terms

Electrical power: The rate at which electrical energy is converted into other forms by an appliance.
Watt: The power of an appliance that converts one joule of electrical energy every second.

2. Power rating of an appliance

“1000 W, 220 V”: when connected to 220 V the appliance converts 1000 J of electrical energy every second.
From the rating: $I = \dfrac{P}{V}$ and $R = \dfrac{V^{2}}{P}$ (R stays the same if the voltage changes).
On a different voltage: $P' = \dfrac{V'^{2}}{R}$ , so $\dfrac{P'}{P} = \left(\dfrac{V'}{V}\right)^{2}$ .
For the same voltage, a higher-power appliance has a lower resistance.

Table of three power ratings with their current and resistance
Rating	Current	Resistance
100 W, 220 V	0.45 A	484 Ω
1000 W, 220 V	4.55 A	48.4 Ω
2200 W, 220 V	10 A	22 Ω

Formulas

Resistance from the rating
$R = \dfrac{V^{2}}{P}$
Power at another voltage
$\dfrac{P'}{P} = \left(\dfrac{V'}{V}\right)^{2}$

Key terms

Power rating: The power an appliance converts when it is connected to its stated (rated) voltage.

3. The kilowatt hour and electricity bills

1 kWh = energy used by a 1 kW appliance in 1 hour $= 1000 \times 3600 = 3.6 \times 10^{6}$ J; the commercial unit of electrical energy.
Units = power (kW) × time (h) × number of appliances × days.
Cost = units × rate per unit.
Energy use depends on power and hours of use; efficient devices (LED lamps) save units.

Table of three ways of using one kilowatt hour
Appliance	Power	Hours	kWh
Electric iron	1 kW	1	1
LED lamp	10 W	100	1
Geyser	2 kW	0.5	1

Formulas

Commercial unit
$1\ \text{kWh} = 3.6 \times 10^{6}\ \text{J}$
Energy in kWh
$\text{units} = P\,(\text{kW}) \times t\,(\text{h})$

Key terms

Kilowatt hour: The electrical energy consumed by an appliance of power one kilowatt working for one hour; it equals 3.6 million joules.

4. Power distribution and house wiring

Generated at about 11 kV → stepped up to about 132 kV → transmission lines → stepped down to 33 kV, then 11 kV, then 220 V for houses. High voltage means low current, so less I²R loss in the lines.
Supply in India: 220 V, 50 Hz AC; live wire at 220 V, neutral at about 0 V.
From the pole: company fuse (in the live wire) → kWh meter → main switch (double pole: breaks live and neutral) → distribution board (a fuse or MCB for each circuit) → circuits.
Appliances are connected in parallel: each gets 220 V and can be switched independently.

Table of voltages at three stages of power distribution
Stage	Voltage
Generation	11 kV
Transmission	132 kV or more
House supply	220 V

Key terms

Distribution board: The box after the main switch from which separate circuits, each with its own fuse or MCB, are taken to different parts of a house.
Double pole main switch: A switch that breaks both the live and the neutral wires at the same time.

5. Fuse, MCB and the ring main

Fuse: a short thin wire of an alloy of low melting point (tin–lead), joined in series in the live wire; it melts when the current exceeds its rating (overload or short circuit). Rating: just above the normal current $I = P/V$ .
MCB (miniature circuit breaker): an automatic switch that trips when the current is too large and can simply be reset.
Switches and fuses in the live wire: when off or blown, the appliance is disconnected from the high potential.
Ring main: a cable (L, N, E) runs from the distribution board round the rooms and back to the board; protected by a 30 A fuse or MCB; sockets in parallel; current reaches each socket by two paths, so a thinner cable will do.

Table comparing a fuse and a miniature circuit breaker
Feature	Fuse	MCB
Action	Wire melts	Switch trips
After a fault	Must be replaced	Reset by hand
Placed in	Live wire	Live wire

Formulas

Normal current, for choosing a fuse
$I = \dfrac{P}{V}$

Key terms

Fuse: A safety device: a short wire of low melting point in the live wire that melts and breaks the circuit when the current exceeds a set value.
Ring main: A household circuit in which a cable loop starting and ending at the distribution board feeds sockets connected in parallel along it.

6. Two-way switch, three-pin plug, earthing and safety

Two-way switch: a common terminal and two contacts. Staircase wiring: live → common of S1; two strap wires join the contacts of S1 and S2; common of S2 → lamp → neutral. Lamp on when both levers are on the same strap; either switch changes it.
Three-pin plug: earth pin longer (connects first, disconnects last) and thicker (cannot enter the L or N hole).
Earthing: the metal body is joined to a copper plate buried in moist ground; a live-to-body fault sends a large current to earth, so the fuse melts.
Colour code (new): live brown, neutral light blue, earth green / green-yellow (old: red, black, green).
Safety: correct fuse rating, no overloading, switch off the mains for repairs, dry hands, earthed metal appliances, good insulation.

Table of the new and old colour codes for house wiring
Wire	New colour	Old colour
Live	Brown	Red
Neutral	Light blue	Black
Earth	Green or green-yellow	Green

Key terms

Earthing: Connecting the metal body of an appliance to the earth through a thick wire and a buried plate, so that a fault current flows to the ground.
Two-way switch: A switch with one common terminal that can be connected to either of two contacts, used in pairs to control one lamp from two places.

Exam tips

Common mistakes

Using watts and minutes when finding kWh.
Assuming an appliance gives its rated power on any voltage.
Putting the fuse or switch in the neutral wire.
Choosing a fuse rating far above the normal current.
Giving only one reason for the shape of the earth pin.

How marks are usually awarded

Bills: units per appliance (1), total units (1), cost (1).
Wiring: correct order of parts and the function of each.
Safety: a reason for each device, linked to the live wire or to earth.

1. Electrical energy and power

Formulas

Key terms

2. Power rating of an appliance

Formulas

Key terms

3. The kilowatt hour and electricity bills

Formulas

Key terms

4. Power distribution and house wiring

Key terms

5. Fuse, MCB and the ring main

Formulas

Key terms

6. Two-way switch, three-pin plug, earthing and safety

Key terms

Exam tips

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