Class 10 Science Chapter 11 — Electricity (International Edition)
NCERT / RBSE Syllabus 2026–27 · Learn by doing · Includes four labelled diagrams and six worked examples
Prepared by: NCERTClasses Team — textbook specialists and experienced teachers.
Based on: NCERT Class 10 Science textbook, Chapter 11, and the Board of Secondary Education, Rajasthan syllabus 2026–27.
Published: 24 September 2026 · Last updated: 24 September 2026
Flip a light switch and the bulb glows instantly — yet the electrons inside the wire actually drift extremely slowly (it can take hours to cross just one metre of wire). So how does light appear so fast?
And why does an electricity bill come in "units" — what exactly is a unit?
- Current: I = Q/t (amperes) · Potential difference: V = W/Q (volts)
- Ohm's law: V = IR — at constant temperature.
- Resistance: R = ρL/A — directly proportional to length, inversely to cross-section.
- Series: R = R1+R2+R3 (same current). Parallel: 1/R = 1/R1+1/R2+1/R3 (same voltage, total resistance less than the smallest resistor).
- Heating effect (Joule's law): H = I²Rt
- Electric power: P = VI = I²R = V²/R · Commercial energy unit: kWh (a "unit")
How to read this — first you think or try it, then comes the explanation:
🔍 Wonder · 🧪 Try it · 📖 Understand · 🔗 Apply · ✅ Check yourself
"Check yourself" has three levels — 1, 2, 3.
Contents
- Foundation check
- Electric current and charge
- Electric potential and potential difference
- Circuit diagrams
- Ohm's law
- Factors affecting resistance — resistivity
- Series combination
- Parallel combination
- Heating effect — Joule's law
- Electric power and energy
- Household electrical safety
- Your ladder
- Marking scheme
- Common mistakes
- Final test
- Glossary
- For parents and teachers
- Beyond NCERT
Foundation check
- What charge does an electron carry?
- Which is a better conductor of electricity — a metal or a non-metal?
- How many watts make one kilowatt?
Answers
1. Negative. 2. A metal. 3. 1000 watts. This chapter examines exactly how the flow of charge becomes current, and how power and energy are correctly calculated.
1. Electric current and charge
🔍 Wonder — Electrons crawl through a wire, yet the bulb lights instantly the moment the switch closes — how?
📖 Understand — The moment the switch closes, every electron in the wire begins moving at once — much like a long pipe already full of water: push water in at one end, and water immediately comes out the other, even though no single drop travelled that whole distance instantly. That's exactly why the bulb lights up right away, even though individual electrons drift slowly.
Electric current (I) is the charge flowing through a conductor's cross-section per second:
I = Q/t
Its unit is the ampere (A). Charge (Q) is measured in coulombs (C), and is always a whole-number multiple of a single electron's charge:
Q = ne
where n is the number of electrons and e is the charge on one electron (1.6 × 10⁻¹⁹ C).
Worth noting — in circuit diagrams, current is always taken to flow from the positive terminal to the negative terminal (conventional current), while electrons actually flow the exact opposite way. This is the single biggest source of confusion — conventional current direction is what's always used in exams and diagrams.
🔗 Apply — A current of 1 ampere means 1 coulomb of charge flows every second — roughly 6.25 × 10¹⁸ electrons per second.
✅ Check yourself
Level 1 What is the unit of electric current? — Answer: Ampere (A).
Level 2 How do conventional current direction and electron flow relate? — Answer: They are exactly opposite — conventional current is taken from positive to negative terminal, while electrons actually flow from negative to positive.
Level 3 A conductor carries 300 C of charge in 5 minutes. Find the current. — Answer: t = 5×60 = 300 seconds. I = Q/t = 300/300 = 1 A.
2. Electric potential and potential difference
📖 Understand — Charge doesn't flow on its own — it needs a "push," which comes from potential difference. The work done in bringing a unit positive charge from infinity to a point is called electric potential. The difference in potential between two points is the potential difference:
V = W/Q
Its unit is the volt (V) — 1 volt means 1 joule of work is needed to move 1 coulomb of charge between two points.
🔗 Apply — A cell or battery maintains this potential difference, continuously pushing charge along — much like a pump pushes water through a pipe.
✅ Check yourself
Level 1 What is the unit of potential difference? — Answer: Volt (V).
Level 2 Define 1 volt. — Answer: If 1 joule of work is required to move 1 coulomb of charge between two points, the potential difference between them is 1 volt.
3. Circuit diagrams
Figure 1 — Simple circuit: an ammeter is always connected in series (directly in the current path), a voltmeter always in parallel (across the resistor).
📖 Understand — An ammeter measures current, so it is always connected in series (so the full current passes through it). A voltmeter measures potential difference, so it is always connected in parallel (so it can measure the potential across that section). This is also why an ammeter is built with very low resistance and a voltmeter with very high resistance — so neither disturbs the circuit's actual behaviour.
✅ Check yourself
Level 1 How is an ammeter connected in a circuit? — Answer: In series.
Level 2 How is a voltmeter connected, and why? — Answer: In parallel, so it can directly measure the potential difference across the two ends of the resistor.
4. Ohm's law
🔍 Wonder — If you keep increasing the potential difference across a conductor, will the current always keep rising in exactly the same proportion?
📖 Understand — Ohm's law states: at constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across it:
V = IR
where R is resistance, measured in ohms (Ω). Plotting V against I gives a straight line through the origin — the line's slope is the resistance.
Worth noting — not every conductor obeys Ohm's law. Devices such as diodes give a V-I graph that isn't a straight line — these are called non-ohmic devices.
Worked example 1: A conductor carries 2 A of current when the potential difference across it is 12 V. Find its resistance.
Solution: R = V/I = 12/2 = 6 Ω.
✅ Check yourself
Level 1 State Ohm's law's formula. — Answer: V = IR.
Level 2 What does the slope of a V-I graph represent? — Answer: Resistance (R).
Level 3 Does a diode obey Ohm's law? — Answer: No — its V-I graph is not a straight line, making it a non-ohmic device.
5. Factors affecting resistance — resistivity
🔍 Wonder — Two wires of the same material, but one thin-and-long, the other thick-and-short — which has higher resistance?
📖 Understand — A conductor's resistance depends on four things:
R = ρL/A
| Factor | Effect |
|---|---|
| Length (L) | Directly proportional — longer wire, higher resistance |
| Cross-sectional area (A) | Inversely proportional — thicker wire, lower resistance |
| Nature of material (ρ) | Every material has its own resistivity — metals low, alloys higher |
| Temperature | In most metals, resistance rises as temperature rises |
Resistivity (ρ) is a property of the material itself — it doesn't change if you change the wire's length or thickness.
| Material | Approx. resistivity (Ω·m) | Used for |
|---|---|---|
| Silver | 1.6 × 10⁻⁸ | Lowest resistivity, but expensive |
| Copper | 1.7 × 10⁻⁸ | Household wiring |
| Nichrome (alloy) | ~100 × 10⁻⁸ | Heaters, irons — deliberately high resistivity |
| Tungsten | ~56 × 10⁻⁸ | Bulb filaments — also needs a very high melting point |
🔗 Apply — Nichrome-type alloys are used in heaters and irons precisely because their resistivity is high (more heat) and they resist oxidising even at very high temperatures.
Worked example 2: A wire is stretched to double its length (volume unchanged). By what factor does its resistance change?
Solution: With volume constant, doubling the length halves the cross-sectional area. Substituting L → 2L and A → A/2 in R = ρL/A: R' = ρ(2L)/(A/2) = 4 × (ρL/A) = 4R — the new resistance is four times the original.
✅ Check yourself
Level 1 How does resistance change with length? — Answer: Directly proportional — resistance rises as length increases.
Level 2 Why is nichrome chosen for heater wires? — Answer: Its resistivity is high (producing more heat), and it resists oxidation even at high temperatures.
Level 3 If a wire's length is tripled by stretching (volume constant), by what factor does its resistance change? — Answer: New A = A/3. R' = ρ(3L)/(A/3) = 9R — nine times.
6. Series combination
Figure 2 — In series, the same current flows through every resistor; total resistance is their sum.
📖 Understand — When resistors are connected one after another along a single path, this is a series combination. Key features:
- The same current (I) flows through all of them.
- Total potential difference is the sum of each resistor's own: V = V1+V2+V3
- Equivalent resistance: R = R1+R2+R3 — always greater than even the largest individual resistor
Worked example 3: Resistors of 2 Ω, 3 Ω and 5 Ω are connected in series to a 10 V battery. Find the current.
Solution: R = 2+3+5 = 10 Ω. I = V/R = 10/10 = 1 A.
🔗 Apply — Old-style decorative fairy lights are often wired in series — that's exactly why one bulb failing goes dark the whole string: the current's only path is broken.
✅ Check yourself
Level 1 What is the formula for equivalent resistance in series? — Answer: R = R1+R2+R3.
Level 2 What stays the same across all resistors in series? — Answer: Current (I).
7. Parallel combination
Figure 3 — In parallel, every resistor shares the same potential difference; current splits across each branch.
📖 Understand — When resistors are connected across the same two points, in separate branches, this is a parallel combination. Key features:
- All of them share the same potential difference (V) — just as every device in a house gets the full 220 V.
- Total current is the sum of each branch's current: I = I1+I2+I3
- Equivalent resistance: 1/R = 1/R1 + 1/R2 + 1/R3 — always less than even the smallest individual resistor
Worked example 4: Resistors of 2 Ω and 3 Ω are connected in parallel. Find the equivalent resistance.
Solution: 1/R = 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Remember — this is the single most common mistake here: the answer is not 5/6, that's 1/R! You must invert it: R = 6/5 = 1.2 Ω.
🔗 Apply — Household wiring is always parallel — that's exactly why one room's bulb blowing doesn't affect the rest of the house, and every appliance gets the full 220 V no matter how many others are running at the same time.
✅ Check yourself
Level 1 What stays the same across all resistors in parallel? — Answer: Potential difference (V).
Level 2 Why isn't household wiring done in series? — Answer: In series, one appliance failing would switch off every appliance, and none would receive the full voltage — parallel wiring lets each appliance run independently, each getting the full voltage.
Level 3 Five resistors, each of resistance R, are connected in parallel. What is the equivalent resistance? — Answer: 1/R_eq = 1/R + 1/R + 1/R + 1/R + 1/R = 5/R. Inverting: R_eq = R/5.
8. Heating effect — Joule's law
🔍 Wonder — An iron or heater's wire glows red-hot, but household wiring doesn't — even though both carry current. Why the difference?
Figure 4 — Practical applications of the heating effect: a nichrome heater coil (deliberately high heat) and a safety fuse (deliberately low melting point).
📖 Understand — When electric current passes through a resistor, some electrical energy converts into heat — this is the heating effect. Joule's law quantifies it:
H = I²Rt
where H is heat (in joules), I is current, R is resistance, t is time (in seconds). Notice — heat is proportional to the square of the current, so doubling the current quadruples the heat produced.
| Practical application | Principle |
|---|---|
| Electric heaters, irons | High-resistivity wire like nichrome, deliberately producing more heat |
| Bulb filament | Tungsten wire heats up enough to glow (emit light) |
| Fuse (safety) | A thin wire with deliberately low melting point — melts and breaks the circuit the instant current exceeds a safe limit, preventing fire or damage |
Worked example 5: A current of 2 A flows through a 5 Ω wire for 10 minutes. Find the heat produced.
Solution: t = 10×60 = 600 seconds. H = I²Rt = (2)² × 5 × 600 = 4 × 5 × 600 = 12,000 joules.
🔗 Apply — Household wiring uses thick, low-resistance copper wire precisely so the heating effect stays negligible in normal use — only the fuse is deliberately thin and low-melting, so it — not the house's actual wiring — is what melts to protect everything else.
✅ Check yourself
Level 1 State Joule's law's formula. — Answer: H = I²Rt.
Level 2 What is deliberately built into a fuse wire? — Answer: A low melting point, so it melts and breaks the circuit if current exceeds a safe limit.
Level 3 If current is tripled, by what factor does heat produced (in the same time) change? — Answer: Heat is proportional to I², so tripling the current gives 9 times the heat.
9. Electric power and energy
📖 Understand — Electric power (P) tells you how fast a device uses electrical energy:
P = VI = I²R = V²/R
Its unit is the watt (W). For measuring energy at scale, kilowatt-hour (kWh) — a "unit" — is used, and it's the basis of electricity bills:
Energy (kWh) = Power (kW) × Time (hours)
Worked example 6 — an electricity bill: A 1000 W heater runs 4 hours a day for a month (30 days). At ₹7 per unit, find the total cost.
Solution: Power = 1000 W = 1 kW. Daily energy = 1 × 4 = 4 kWh (4 units). Monthly consumption = 4 × 30 = 120 units. Total cost = 120 × 7 = ₹840.
🔗 Apply — This same calculation shows which household appliances actually drive up a bill — both higher power (W) and longer usage time matter together. A low-power LED bulb running all day can still use far fewer units than a heater running just a couple of hours.
✅ Check yourself
Level 1 What is the commercial unit of electrical energy? — Answer: Kilowatt-hour (kWh), called a "unit."
Level 2 A 2000 W geyser runs 30 minutes daily — how many units does it use per day? — Answer: 2 kW × 0.5 hour = 1 unit per day.
Level 3 Five 100 W bulbs run 6 hours daily, and a 1500 W AC runs 3 hours daily. Find the total units and cost for a month (30 days) at ₹7/unit. — Answer: Bulbs: 5×100=500W=0.5kW; daily 0.5×6=3 kWh. AC: 1.5kW; daily 1.5×3=4.5 kWh. Daily total = 3+4.5 = 7.5 kWh. Monthly = 7.5×30 = 225 units. Cost = 225×7 = ₹1,575.
10. Household electrical safety — short-circuiting and overloading
📖 Understand — Household wiring faces two common hazards:
| Hazard | What happens | Result |
|---|---|---|
| Short-circuiting | When the live and neutral wires touch directly, with no appliance/resistance between them | Resistance drops to nearly zero, current suddenly spikes, generating intense heat (H=I²Rt) — a fire risk |
| Overloading | When far too many appliances are run at once on the same parallel line | Total current exceeds the wire's safe limit, and the wire can overheat or even melt |
🔗 Apply — This is exactly why every home's main line has a fuse or MCB (Miniature Circuit Breaker) — in either situation, it automatically breaks the circuit the instant current crosses the safe limit, before the wiring can overheat dangerously.
✅ Check yourself
Level 1 Why does current spike suddenly in a short circuit? — Answer: Because the wires touching directly makes resistance nearly zero, and by V=IR, low resistance means very high current.
Level 2 What is installed to prevent overloading? — Answer: A fuse or MCB.
Your ladder
| Level | Total | If you got this many right | You are |
|---|---|---|---|
| Level 1 | 13 | 10+ | Familiar |
| Level 2 | 13 | 9+ | Proficient — board-exam ready |
| Level 3 | 6 | 4+ | Skilled |
Marking scheme
(An example of a typical examiner's approach — not an official scheme.)
Question (5 marks): Resistors of 4 Ω, 6 Ω and 12 Ω are connected in parallel across a 12 V battery. Find the equivalent resistance, total current, and current through each branch.
Correctly setting up 1/R. 1 mark
Correctly inverting to find R. 1 mark
Calculating total current. 1 mark
Finding each branch's current separately. 2 marks
Common mistakes
| Common mistake | Correct fact |
|---|---|
| Taking 1/R as the final answer in parallel combinations | You must invert it — R = 1/(1/R). |
| "Electrons flow from positive to negative" | Electrons flow from negative to positive; conventional current is taken as the opposite. |
| "Ammeter goes in parallel, voltmeter in series" | The reverse — ammeter in series, voltmeter in parallel. |
| Plugging time in minutes/hours directly into formulas | In H=I²Rt, time must always be in seconds. |
| "Every conductor obeys Ohm's law" | Devices like diodes are non-ohmic. |
Final test — mixed
10+ correct = chapter mastered.
- State the formula for electric current.
- What is Ohm's law's formula?
- How is an ammeter connected in a circuit?
- How does resistance change with length?
- What is the formula for equivalent resistance in series?
- What is always true of equivalent resistance in parallel?
- State Joule's law.
- State the formula for electric power (in three forms).
- What is the unit of an electricity bill?
- What is deliberately built into a fuse wire?
- (Chapter 10) Which lens corrects myopia?
- (Chapter 9) State the lens formula.
Answers — 1. I=Q/t | 2. V=IR | 3. In series | 4. Directly proportional (increases) | 5. R=R1+R2+R3 | 6. Always less than the smallest individual resistor | 7. H=I²Rt | 8. P=VI=I²R=V²/R | 9. Kilowatt-hour (kWh/unit) | 10. Low melting point | 11. Concave lens | 12. 1/v−1/u=1/f
Glossary
| English | Hindi | English | Hindi |
|---|---|---|---|
| Electric current | विद्युत धारा | Series combination | श्रेणीक्रम |
| Potential difference | विभवांतर | Parallel combination | पार्श्वक्रम |
| Resistance | प्रतिरोध | Heating effect | तापीय प्रभाव |
| Resistivity | प्रतिरोधकता | Electric power | विद्युत शक्ति |
| Ammeter | अमीटर | Kilowatt-hour | किलोवाट-घंटा |
| Voltmeter | वोल्टमीटर | Fuse | फ़्यूज़ |
For parents and teachers
Five-minute check: Have them write out Ohm's law, the series/parallel formulas, and Joule's law. Ask which order household wiring uses, and why. Walk through an electricity bill calculation together.
To try at home: note down the watt ratings printed on 3-4 household appliances, and have them calculate the daily/monthly unit cost themselves — a direct, real-world connection to the chapter.
Beyond NCERT — For Curious Readers
This section goes beyond the RBSE/NCERT Class 10 syllabus and is not required for the board exam. It draws only on government and internationally reputed university sources, for curious readers who want to see where this chapter leads.
Volta's first battery
In 1800, Italian scientist Alessandro Volta stacked alternating discs of silver and zinc separated by cloth soaked in salt solution, building the "voltaic pile" — historians regard it as the first device to produce a steady, continuous electric current. Before this, scientists only had access to brief static-electricity shocks; Volta's invention made it possible, for the first time, to experiment with a continuously flowing current — exactly the kind of current this chapter teaches. The unit of potential, the "volt," is named after him.
Ohm's discovery was initially rejected
German physicist Georg Simon Ohm published his now-famous law in 1827, but the German scientific community of the time received it very coldly — some historians describe it as being nearly dismissed outright, leaving Ohm discouraged enough to leave academic life for a period. Years later, once his work gained recognition in Britain and the rest of Europe, he finally received proper credit — the unit of resistance, the "ohm," bears his name today.
Edison versus Tesla — the historic War of the Currents
In the 1880s, Thomas Edison championed direct current (DC), while Nikola Tesla and George Westinghouse promoted alternating current (AC) — history calls this the "War of the Currents." AC ultimately won, because a transformer can easily change its voltage, making it possible to transmit electricity over long distances with far less energy loss. Today, this same AC electricity powers homes worldwide, including India's own national grid.
India's National Grid
India's Central Electricity Authority oversees the country's unified "One Nation, One Grid" network, connecting nearly the entire nation. From generation to reaching every home, it runs on exactly the same principles of current, potential difference and resistance this chapter introduces — just applied at an enormously larger scale.
Smart meters — the digital future of electricity billing
Traditional electricity meters were read once a month, but modern smart meters record consumption every hour (or even more frequently) and transmit it directly to the utility — built on exactly the same P=VI principle covered in this chapter, just measured automatically and continuously. India's Ministry of Power runs a major nationwide smart-metering programme, aiming to let consumers see their real-time consumption and to improve monitoring against electricity theft.
Sources for this section
- ncert.nic.in — NCERT, Government of India
- ePathshala — Ministry of Education, Government of India
- cea.nic.in — Central Electricity Authority, Government of India
Note: nothing from these sources has been copied into this text; all statements above are written in the author's own words for general educational understanding, and are not professional or engineering advice.
Continue reading
← Previous: Chapter 10 — The Human Eye and the Colourful World (4 marks)
→ Next: Chapter 12 — Magnetic Effects of Electric Current (6 marks)
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- Chapter 10 — The Human Eye and the Colourful World (English)
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Based on the Class 10 Science (Code 07) syllabus 2026–2027 of the Board of Secondary Education, Rajasthan, Ajmer — Chapter 11, marks weightage 7. Textbook: Science, NCERT. All diagrams are original.
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