CDS Physics · Electricity and Magnetism

Electric Power and Home Wiring

Electric power and the heating effect, the kilowatt-hour on the electricity bill, fuses, short circuits and the three wires of a house, and what a bulb does with energy.

All Electricity and Magnetism notes

Why this matters

Twelve CDS questions from 2018 (I) to 2025 (I), seven of them EASY. Five are short sums (power, units of energy, how many bulbs a fuse allows), four ask about fuses, short circuits and the wires of the mains, and three ask who found the heating effect, why a bulb holds argon, and which device does not turn electricity into light. The units sum for a 100 W bulb burning 10 hours a day has come twice.

Concept 1 of 4: Electric power and the heating effect

Power is the energy used each second. For an electric device it is the voltage times the current. Put Ohm's law into that and you get two more forms: one for when you know the current, one for when you know the voltage. A bulb's filament keeps (nearly) the same resistance, so if the voltage falls, the power falls with the square of the voltage. The heat a current makes in a wire was measured by James Prescott Joule.

Definition

The rules:

$P = VI = I^{2}R = \dfrac{V^{2}}{R}$ . One watt is one joule per second.
A rating such as "60 W, 220 V" fixes the resistance: $R = \dfrac{V^{2}}{P}$ .
On another voltage $V'$ , with $R$ fixed: $P' = P\left(\dfrac{V'}{V}\right)^{2}$ . Half the voltage gives a quarter of the power.
Joule's law of heating: $H = I^{2}Rt$ .
Same current (series): the bigger resistance heats more. Same voltage (parallel): the smaller resistance heats more.
A higher-wattage bulb on the same voltage has a lower resistance (a thicker filament).

Electric power and Joule heating

P = VI = I^{2}R = \dfrac{V^{2}}{R} \qquad H = I^{2}Rt \qquad P' = P\left(\dfrac{V'}{V}\right)^{2}

Ppower in watts
Hheat produced in time t, in joules
P′, V′power at a voltage other than the rated one

Worked example

An electric iron is rated 1000 W, 250 V. Find its resistance and the current it draws at the rated voltage. What power does it give on a 200 V supply?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2025 · CDS (I) 2025 — General Knowledge · Q28Moderate

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

A light bulb rated as 60 W at 220 V has a potential difference of 110 V across its ends. The power dissipated in this light bulb is :

The resistance stays fixed, not the power

A bulb's rating tells you its resistance. On a lower voltage, work out

V^{2}/R

again. At half the voltage the power is one quarter, not one half.

More watts means less resistance

On the same voltage,

R = V^{2}/P

. So a 100 W bulb has a smaller resistance than a 25 W bulb. Students often guess the opposite.

Drill 2 more on electric power and the heating effect

Concept 2 of 4: Electrical energy and the unit on the bill

Energy is power multiplied by time. The joule is far too small for a household, so the electricity board counts in kilowatt-hours, which the bill calls units. One unit is what a 1000 W device uses in one hour.

Definition

The rules:

$E = Pt$ .
1 unit = 1 kilowatt-hour (kWh) $= 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^{6}$ J.
Units used = power in kilowatts × time in hours. Change watts to kilowatts first (divide by 1000).
For several days, find one day's units and multiply by the number of days.
Bill = units × rate per unit.

Electrical energy

E = Pt \qquad 1\ \text{kWh} = 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^{6}\ \text{J}

Eenergy used
Ppower (in kW for units)
ttime (in hours for units)

Worked example

A house runs a 1.5 kW geyser for 2 hours a day and four 40 W tube lights for 5 hours a day. How many units does it use in 30 days, and what is the bill at ₹6 per unit?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2019 · CDS (II) 2019 — General Knowledge · Q46Moderate

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

A 100 W electric bulb is used for 10 hours a day. How many units of energy are consumed in 30 days?

Kilowatts times hours, not watts times hours

A unit is a kilowatt-hour. Divide the watts by 1000 before you multiply by the hours, or the answer comes out 1000 times too big.

A unit is energy, not power

The kWh measures energy (power × time). The kW measures power. A bill charges for energy, so it counts kWh.

Drill 1 more on electrical energy and the unit on the bill

Concept 3 of 4: Fuses, short circuits and house wiring

Indian homes get alternating current at 220 V. Three wires come in: the live wire carries the supply, the neutral wire completes the path, and the earth wire is a safety path to the ground. A fuse is a short piece of thin wire that melts and breaks the circuit when the current gets too big. That happens in a short circuit, when the live and neutral wires touch and the resistance drops almost to zero, or when too many devices run from one line.

Definition

What to know:

Supply: AC, 220 V (r.m.s.), 50 Hz. The peak voltage is $220\sqrt{2} \approx 311$ V.
Fuse: a wire of low melting point (an alloy of tin and lead) placed in the live wire. It melts by the heating effect when the current goes above its rating.
Largest safe power on a fuse $= V \times$ its rating. Number of equal devices in parallel = that power ÷ the power of one device (round down).
Short circuit: live touches neutral, resistance falls nearly to zero, current shoots up. Overloading: too many devices on one line.
Earthing: the metal body of an appliance is joined to the earth wire, so a leak sends current into the ground, not through the person touching it.
An MCB (miniature circuit breaker) switches off by itself on too much current and is reset instead of replaced.

Wire or part	Fact
Live and neutral	220 V r.m.s. between themQ CDS 2023 (I): the r.m.s. voltage between live and neutral in Indian homes is 220 V.
Live wire	Red insulation (the code in NCERT); the fuse and switch go in it
Neutral wire	Black insulation (the code in NCERT)
Earth wire	Green insulation; joined to the metal body of an applianceQ CDS 2022 (I): a green wire is the earth wire, not the live wire.
Fuse	Low melting point wire in the live line; melts when the current is too bigQ CDS 2018 (II): a 5 A fuse at 220 V allows 1100 W, so eleven 100 W bulbs.
Short circuit	Live meets neutral; the current rises sharply and the fuse blows

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2022 · CDS (I) 2022 — General Knowledge · Q3Easy

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

At the time of short-circuit, the current in the circuit :

Green is the earth wire

In the colour code NCERT uses, red is live, black is neutral and green is earth. Never take the green wire for the live one.

The fuse goes in the live wire

A fuse in the neutral wire would blow but leave the appliance still joined to the live supply, which is dangerous. The fuse and the switch always go in the live wire.

220 V is the r.m.s. value

The 220 V of the mains is its r.m.s. value. The voltage swings up to a peak of about 311 V (

220\sqrt{2}

Drill 4 more on fuses, short circuits and house wiring

Concept 4 of 4: Bulbs and energy changes

Every electric device turns electrical energy into some other form: light, heat, motion or sound. A filament bulb makes light by heating a thin tungsten wire until it glows, so most of its energy comes out as heat. The bulb is filled with an inert gas so the hot tungsten does not burn away quickly.

Definition

What to know:

A filament bulb uses tungsten (melting point about 3400 °C).
It is filled with an inert gas (argon, sometimes nitrogen) that stops the hot filament from oxidising and slows its evaporation, so the bulb lasts longer.
An LED gives light with very little heat, so it wastes far less energy.
A candle turns chemical energy into heat and light; no electricity is involved.

Device	Energy change
Filament bulb	Electrical to light, and much more heat
LED	Electrical to light, very little heat
Laser	Electrical to a narrow beam of light of one colour
Television set	Electrical to light and sound
Electric heater or iron	Electrical to heat
Electric motor or fan	Electrical to mechanical
Candle	Chemical to heat and lightQ CDS 2018 (II): the candle is the one that does not turn electrical energy into light.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2018 · CDS (I) 2018 — General Knowledge · Q6Easy

Example 4 · Electricity and Magnetism · Electric Power and Home Wiring

Why is argon gas used along with tungsten wire in an electric bulb?

The gas in a bulb is for a longer life

Argon is inert. It keeps the hot tungsten from oxidising and slows its evaporation, so the bulb lasts longer. It does not cut the power used or colour the light.

Drill 1 more on bulbs and energy changes

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 and the heating effect
Electric power and Joule heating
$P = VI = I^{2}R = \dfrac{V^{2}}{R} \qquad H = I^{2}Rt \qquad P' = P\left(\dfrac{V'}{V}\right)^{2}$
Electrical energy and the unit on the bill
Electrical energy
$E = Pt \qquad 1\ \text{kWh} = 1000\ \text{W} \times 3600\ \text{s} = 3.6 \times 10^{6}\ \text{J}$

Reference tables (2)

Fuses, short circuits and house wiring6 rows

Wire or part	Fact
Live and neutral	220 V r.m.s. between themQ CDS 2023 (I): the r.m.s. voltage between live and neutral in Indian homes is 220 V.
Live wire	Red insulation (the code in NCERT); the fuse and switch go in it
Neutral wire	Black insulation (the code in NCERT)
Earth wire	Green insulation; joined to the metal body of an applianceQ CDS 2022 (I): a green wire is the earth wire, not the live wire.
Fuse	Low melting point wire in the live line; melts when the current is too bigQ CDS 2018 (II): a 5 A fuse at 220 V allows 1100 W, so eleven 100 W bulbs.
Short circuit	Live meets neutral; the current rises sharply and the fuse blows

Bulbs and energy changes7 rows

Device	Energy change
Filament bulb	Electrical to light, and much more heat
LED	Electrical to light, very little heat
Laser	Electrical to a narrow beam of light of one colour
Television set	Electrical to light and sound
Electric heater or iron	Electrical to heat
Electric motor or fan	Electrical to mechanical
Candle	Chemical to heat and lightQ CDS 2018 (II): the candle is the one that does not turn electrical energy into light.

Watch out for (8)

The resistance stays fixed, not the power
→ Electric power and the heating effect
More watts means less resistance
→ Electric power and the heating effect
Kilowatts times hours, not watts times hours
→ Electrical energy and the unit on the bill
A unit is energy, not power
→ Electrical energy and the unit on the bill
Green is the earth wire
→ Fuses, short circuits and house wiring
The fuse goes in the live wire
→ Fuses, short circuits and house wiring
220 V is the r.m.s. value
→ Fuses, short circuits and house wiring
The gas in a bulb is for a longer life
→ Bulbs and energy changes

Test yourself on Electricity and Magnetism

15 past CDS questions from this chapter, timed at 15 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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