Science · Physics · Class 10 · CBSE

Electricity

From electric charge to household circuits — master every concept, formula and numerical for Class 10 board exams.

20+ Key Formulae

8 Core Concepts

15+ MCQ Questions

100% Board Coverage

What is Electric Charge?

Electric charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. Charge can be positive (protons) or negative (electrons). Like charges repel; unlike charges attract.

Analogy

Think of charge like magnetic poles on a fridge magnet — two north poles push apart, but a north and south pull together. Charge works exactly the same way, just for electricity.

The SI unit of charge is the Coulomb (C). One Coulomb is an enormous amount of charge — the charge of about 6.24 × 10¹⁸ electrons. In everyday circuits, we deal with charges in the range of microcoulombs (µC).

Charge is conserved — it can neither be created nor destroyed, only transferred.
Charge of one electron = −1.6 × 10⁻¹⁹ C; charge of one proton = +1.6 × 10⁻¹⁹ C.
A body is neutral when it has equal numbers of protons and electrons.
Conductors allow free movement of electrons; insulators do not.
Static electricity involves accumulation of charge without current flow.

Electric Current

Electric current is the rate of flow of electric charge through a conductor. It is the ordered movement of free electrons in a metallic conductor under the influence of an electric field.

Analogy

Current is like water flowing through a pipe. The amount of water passing a point per second is like the charge passing a cross-section per second. A wider pipe (thicker wire) carries more water (current).

Conventional current flows from positive to negative terminal (opposite to electron flow). This historical convention was set before the discovery of electrons and is still used universally.

Formula: I = Q / t, where I = current (A), Q = charge (C), t = time (s).
SI unit of current is Ampere (A). 1 A = 1 C/s.
Measured using an Ammeter connected in SERIES in a circuit.
Ammeter has very low resistance so it does not disturb the circuit.
Direction of conventional current: positive terminal → external circuit → negative terminal.

Electric Current Formula

\[ I = \frac{Q}{t} \]

I

Electric current in Amperes (A) — the rate of charge flow

Q

Electric charge in Coulombs (C) — total charge that flows

t

Time in seconds (s) — duration of charge flow

A

Ampere

SI unit of current (1 A = 1 C/s)

C

Coulomb

SI unit of charge

s

Second

SI unit of time

mA

Milliampere

1 mA = 10⁻³ A (used for small currents)

Electric Potential & Potential Difference

Electric potential at a point is the work done per unit charge to bring a positive test charge from infinity to that point. Potential difference (voltage) between two points is the work done per unit charge to move charge from one point to the other.

Analogy

Think of potential difference like the height difference between two water tanks. Water naturally flows from the higher tank (high potential) to the lower one (low potential) — just as current flows from high potential to low potential.

A battery maintains a potential difference between its terminals using chemical energy. This potential difference (called EMF) drives the current through the circuit.

Formula: V = W / Q, where V = potential difference (V), W = work done (J), Q = charge (C).
SI unit of potential difference is Volt (V). 1 V = 1 J/C.
Measured using a Voltmeter connected in PARALLEL across a component.
Voltmeter has very high resistance so negligible current flows through it.
EMF (Electromotive Force) is the potential difference across a battery when no current flows.

Potential Difference Formula

\[ V = \frac{W}{Q} \]

V

Potential difference in Volts (V) — the 'pressure' that drives current

W

Work done in Joules (J) — energy used to move the charge

Q

Charge in Coulombs (C) — amount of charge being moved

V

Volt

SI unit of potential difference (1 V = 1 J/C)

J

Joule

SI unit of energy / work done

kV

Kilovolt

1 kV = 1000 V (used in power transmission)

mV

Millivolt

1 mV = 10⁻³ V (used in biological signals)

Resistance & Ohm's Law

Resistance is the property of a conductor by virtue of which it opposes the flow of electric current through it. Ohm's Law states that the current through a conductor is directly proportional to the potential difference across it, provided temperature remains constant.

Analogy

Resistance is like friction in a pipe. A narrow, rough pipe resists water flow more than a wide, smooth one. In a wire, thicker wires and better conductors have lower resistance.

Ohm's Law is not a universal law — it applies only to ohmic conductors (like metallic wires at constant temperature). Non-ohmic devices like diodes, LEDs, and thermistors do NOT obey Ohm's Law.

Ohm's Law: V = IR (Voltage = Current × Resistance).
SI unit of resistance is Ohm (Ω). 1 Ω = 1 V/A.
A conductor obeys Ohm's Law if the V–I graph is a straight line through the origin.
Resistance depends on: length (L), cross-sectional area (A), material (ρ), and temperature.
Formula for resistance: R = ρL/A, where ρ is resistivity of the material.

Ohm's Law

\[ V = IR \quad \Rightarrow \quad I = \frac{V}{R} \quad \Rightarrow \quad R = \frac{V}{I} \]

V

Potential difference across the conductor in Volts (V)

I

Current flowing through the conductor in Amperes (A)

R

Resistance of the conductor in Ohms (Ω)

Ω

Ohm

SI unit of resistance (1 Ω = 1 V/A)

kΩ

Kilohm

1 kΩ = 1000 Ω

MΩ

Megaohm

1 MΩ = 10⁶ Ω (insulators)

mΩ

Milliohm

1 mΩ = 10⁻³ Ω (superconductors ~0)

Resistivity Formula

\[ R = \rho \frac{L}{A} \]

R

Resistance of the conductor in Ohms (Ω)

ρ

Resistivity (specific resistance) of the material in Ω·m — depends only on material and temperature, not shape

L

Length of the conductor in metres (m) — resistance increases with length

A

Cross-sectional area in m² — resistance decreases with thicker wire

Ω·m

Ohm-metre

SI unit of resistivity

m

Metre

SI unit of length

m²

Square metre

SI unit of area

S/m

Siemens/metre

SI unit of conductivity (= 1/ρ)

Resistivity of Common Materials

1.7×10⁻⁸

Resistivity of Copper (Ω·m)

Excellent conductor — used in wires

2.8×10⁻⁸

Resistivity of Aluminium (Ω·m)

Good conductor — used in power lines

10⁶–10¹⁴

Resistivity of Insulators (Ω·m)

Glass, rubber, plastic

1.0×10⁻⁶

Resistivity of Nichrome (Ω·m)

Used in heating elements

~0

Resistivity of Superconductors

Near absolute zero temperature

100×

Resistance increases when heated

Due to more lattice vibrations

Series vs Parallel Circuits

Feature	Series Circuit	Parallel Circuit
Connection	Components connected end-to-end	Components connected across same two points
Current	Same through all components (I = I₁ = I₂)	Divides — different through each branch
Voltage	Divides — V = V₁ + V₂ + V₃	Same across all components (V = V₁ = V₂)
Total Resistance	R = R₁ + R₂ + R₃ (always increases)	1/R = 1/R₁ + 1/R₂ (always decreases)
Failure effect	All components stop if one fails	Others continue working if one fails
Brightness of bulbs	Dimmer (current shared with resistance)	Same brightness as individual bulb
Household use	Not used — failure stops everything	Used — each appliance works independently
Equivalent R	Always greater than largest R	Always less than smallest R

Resistors in Series

\[ R_s = R_1 + R_2 + R_3 + \cdots + R_n \]

Rₛ

Total (equivalent) resistance of series combination in Ω

R₁…Rₙ

Individual resistances in Ω — their sum gives total resistance

Note

In series: same current flows through all resistors. Voltage divides proportionally to resistance.

V = V₁+V₂+V₃

Voltage law (series)

Voltages add up across all resistors

I = I₁=I₂=I₃

Current law (series)

Current is the same through each resistor

Rₛ > R_max

Series always larger

Equivalent resistance exceeds any individual R

Resistors in Parallel

\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \]

Rₚ

Total (equivalent) resistance of parallel combination in Ω

1/R₁…

Reciprocals of individual resistances — their sum gives 1/Rₚ

Note

For two resistors in parallel: Rₚ = (R₁ × R₂) / (R₁ + R₂)

V = V₁=V₂=V₃

Voltage law (parallel)

Same voltage across all parallel branches

I = I₁+I₂+I₃

Current law (parallel)

Total current = sum of branch currents

Rₚ < R_min

Parallel always smaller

Equivalent R is less than any individual R

Interactive: Ohm's Law Calculator

Adjust voltage (V) and resistance (R) using the sliders to see how current (I) changes in real time.

\( I = V / R \)

V (Voltage)

12 V

Potential difference across the resistor

R (Resistance)

100 Ω

Resistance of the conductor

Current I =

— A

Interactive: Series Resistance Calculator

Add up to three resistors in series and see the total equivalent resistance instantly.

\( Rs = R1 + R2 + R3 \)

R₁

10 Ω

First resistor

R₂

20 Ω

Second resistor

R₃

30 Ω

Third resistor

Total Series Resistance Rₛ =

— Ω

Heating Effect of Electric Current

When electric current flows through a resistor, electrical energy is converted into heat energy due to the collisions of electrons with the lattice ions of the conductor. This is called the Joule Heating Effect or Joule's Law.

Analogy

Think of electrons as billiard balls rushing through a crowded room of people (ions). Every collision transfers energy as heat. The more crowded (higher resistance) or faster moving (higher current), the more heat produced.

The heating effect is the basis of electric heaters, incandescent bulbs, fuses, and geysers. However, in computer chips and motors, this heat is wasted energy that engineers work hard to minimise.

Joule's Law: H = I²Rt — Heat produced is proportional to square of current.
Heat is also expressed as: H = VIt = V²t/R.
A fuse wire has high resistance and low melting point — it melts and breaks the circuit when current is too high.
MCB (Miniature Circuit Breaker) is a modern, resettable alternative to fuses.
Electric bulb filament is made of tungsten — high melting point (3380°C) so it glows without melting.

Joule's Law of Heating

\[ H = I^2 R t = VIt = \frac{V^2 t}{R} \]

H

Heat produced in Joules (J)

I

Current through the conductor in Amperes (A)

R

Resistance of the conductor in Ohms (Ω)

t

Time for which current flows in seconds (s)

V

Potential difference across the conductor in Volts (V)

J

Joule

SI unit of heat / energy

cal

Calorie

1 cal = 4.2 J (older unit of heat)

kWh

Kilowatt-hour

Practical unit: 1 kWh = 3.6 × 10⁶ J

W

Watt

SI unit of power: 1 W = 1 J/s

Electric Power

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

P

Electric power in Watts (W) — rate of energy consumption

V

Potential difference in Volts (V)

I

Current in Amperes (A)

R

Resistance in Ohms (Ω)

Note

Power = Energy / Time → P = H/t. Also: Energy = P × t = VIt

W

Watt

SI unit of power: 1 W = 1 V × 1 A

kW

Kilowatt

1 kW = 1000 W (used for appliances)

HP

Horsepower

1 HP = 746 W (used for motors)

kWh

Unit of electrical energy (1 unit = 1 kWh)

Interactive: Electric Power Calculator

Adjust voltage and current to calculate power consumed by an appliance.

\( P = V × I \)

V (Voltage)

220 V

Supply voltage (India standard = 220 V)

I (Current)

5 A

Current drawn by appliance

Power P =

— W

V–I Graph: Ohmic vs Non-Ohmic Conductors

For an ohmic conductor (metallic wire), the V–I graph is a straight line through the origin. For a non-ohmic device (e.g. diode), the graph is a curve.

Source: Illustrative — based on Class 10 NCERT Chapter 12

Power Ratings of Common Household Appliances

Comparison of power consumption (in Watts) of common household electrical appliances at 220 V supply.

Source: Typical rated values for Indian households

Resistivity Comparison of Materials

Relative resistivity of different materials (log scale approximation for comparison). Silver and copper are best conductors; insulators have extremely high resistivity.

Source: Standard material data — NCERT Physics

How Does a Simple Electric Circuit Work?

1

Battery provides potential difference Energy Source

The battery (cell) converts chemical energy into electrical energy, creating a potential difference (voltage) between its positive (+) and negative (−) terminals.

2

Switch closes the circuit Control

When the switch is closed, it creates a conducting path. An open switch breaks the path and stops current flow.

3

Free electrons begin to drift Charge Flow

The electric field set up by the battery causes free electrons in the metallic wire to drift from the negative terminal through the external circuit to the positive terminal.

4

Current flows (conventional) Current Direction

Conventional current flows in the opposite direction — from positive terminal, through the circuit, to the negative terminal. This is the direction shown in circuit diagrams.

5

Resistor opposes current — produces heat Energy Conversion

As electrons pass through the resistor, they collide with ions. This converts electrical energy into heat (Joule heating). Bulb filaments glow because of this heating effect.

6

Energy is returned to battery Energy Supply

The battery continuously maintains the potential difference through chemical reactions, supplying energy to keep the current flowing until the battery is exhausted.

History of Electricity — Key Discoveries

600 BC

Thales of Miletus

Observed that rubbed amber attracted light objects — earliest known observation of static electricity.

1600 AD

William Gilbert

Coined the term 'electricus' from the Greek word for amber; distinguished electricity from magnetism.

1752

Benjamin Franklin

Proved lightning is electrical in nature using his famous kite experiment; invented the lightning rod.

1800

Alessandro Volta

Invented the voltaic pile — the world's first electric battery, producing steady current from chemical reactions.

1820

Hans Christian Ørsted

Discovered that electric current produces a magnetic field — establishing the link between electricity and magnetism.

1827

Georg Simon Ohm

Formulated Ohm's Law (V = IR), relating voltage, current and resistance in conductors.

1831

Michael Faraday

Discovered electromagnetic induction — the principle behind generators and transformers.

1841

James Prescott Joule

Established the law of heating effect of current (Joule's Law: H = I²Rt).

1879

Thomas Edison

Invented the practical incandescent light bulb; established the first commercial electrical power distribution system.

1888

Nikola Tesla

Developed AC (alternating current) system and AC induction motor, leading to modern power transmission.

Ammeter vs Voltmeter

Feature	Ammeter	Voltmeter
Purpose	Measures electric current	Measures potential difference (voltage)
Connection	In SERIES with the circuit	In PARALLEL across the component
Resistance	Very LOW (ideally zero)	Very HIGH (ideally infinite)
Why that resistance	Low R so it doesn't reduce current	High R so it doesn't draw significant current
Unit	Ampere (A)	Volt (V)
Symbol in diagram	A in a circle	V in a circle
Effect on circuit	Negligible (due to low R)	Negligible (due to high R)

Circuit Diagram: Series and Parallel Resistors

Left: Three resistors R₁, R₂, R₃ in series with a battery. Right: Three resistors in parallel.

Important Facts & Exam Traps

💡

Did You Know?

The electricity bill you pay at home is for energy in 'units'. 1 unit = 1 kWh. If a 1000 W geyser runs for 1 hour, it consumes exactly 1 unit of energy. At ₹6 per unit, that's ₹6 for one hot shower!

✗

Common Mistake

Students often say 'current flows through the voltmeter'. This is WRONG — a voltmeter has very high resistance so nearly zero current flows through it. It measures voltage, not current.

✓

Exam Tip — Memory Formula

Remember V = IR using the VIR triangle: cover the quantity you want — V = I×R, I = V÷R, R = V÷I. This one triangle solves every Ohm's Law numerical in 3 seconds!

⚠

Misconception Alert

Current does NOT get 'used up' in a resistor. The same amount of current enters and leaves a resistor. What gets used up is ENERGY (voltage drops). Confusing current and energy is a top board exam mistake.

✓

Exam Tip — Resistors

When resistors are connected in parallel and one of them is removed, the total resistance INCREASES and total current DECREASES. This surprises many students — trace it through using the parallel formula.

💡

Why Do Birds Sit on High-Voltage Wires?

Birds are safe because both feet are at the same potential — no potential difference means no current through the bird. The moment a bird touches two wires of different potential (or the wire and a grounded pole), current flows and it can be electrocuted.

Key Terms & Definitions

Electric Charge

Greek: 'elektron' (amber)

A fundamental property of matter that causes electromagnetic interactions. Measured in Coulombs (C).

An electron has charge −1.6 × 10⁻¹⁹ C.

Electric Current

Latin: 'currere' (to run)

Rate of flow of electric charge. I = Q/t. Measured in Amperes (A).

A 60 W bulb at 220 V draws about 0.27 A current.

Potential Difference

Latin: 'potentia' (power)

Work done per unit charge to move charge between two points. V = W/Q. Measured in Volts (V).

A torch battery has 1.5 V potential difference.

Resistance

Latin: 'resistere' (to withstand)

Opposition offered by a conductor to the flow of current. R = V/I. Measured in Ohms (Ω).

A nichrome wire of 1 m length has ~110 mΩ resistance.

Resistivity

Derived from 'resistance'

Intrinsic property of a material representing its resistance per unit length per unit cross-section. ρ = RA/L.

Copper: ρ = 1.7 × 10⁻⁸ Ω·m; Glass: ρ ≈ 10¹² Ω·m.

Ohm's Law

Named after Georg Simon Ohm

At constant temperature, V ∝ I, i.e. V = IR for ohmic conductors.

10 Ω resistor at 5 V → current = 0.5 A.

Joule's Law

Named after James Prescott Joule

Heat produced in a conductor: H = I²Rt. Heat is proportional to square of current, resistance, and time.

5 A through 10 Ω for 2 s → H = 500 J.

Electric Power

Greek: 'dynamis' (power)

Rate of doing work or rate of energy consumption. P = VI = I²R = V²/R. Measured in Watts (W).

A 220 V, 5 A heater has power = 1100 W = 1.1 kW.

EMF

Electromotive Force

The potential difference across a cell/battery when no current is drawn from it (open circuit voltage).

A fresh 1.5 V cell has EMF = 1.5 V.

Fuse

Latin: 'fusus' (melted)

A safety device — thin wire of low melting point and high resistance that melts and breaks circuit during overcurrent.

A 5 A fuse melts if current exceeds 5 A.

Ammeter

Ampere + meter

Instrument to measure electric current. Connected in series. Has very low resistance.

Always connect ammeter in series — never in parallel.

Voltmeter

Volt + meter

Instrument to measure potential difference. Connected in parallel. Has very high resistance.

Connected across the resistor/component, not in series.

Match: Formula to Quantity

🖱 Desktop: drag a term onto a definition | 📱 Mobile: tap a term, then tap its definition

Drag each formula on the left to its correct quantity on the right. On mobile, tap a formula then tap the definition.

① Terms — tap or drag

I = Q / t

V = W / Q

R = V / I

R = ρL / A

H = I²Rt

P = VI

Rₛ = R₁+R₂+R₃

1/Rₚ = 1/R₁+1/R₂

② Definitions — drop or tap here

Electric Current

Potential Difference

Resistance (Ohm's Law)

Heat produced (Joule's Law)

Parallel Resistance

Resistance from material & dimensions

Electric Power

Series Resistance

Match: Device to Purpose

🖱 Desktop: drag a term onto a definition | 📱 Mobile: tap a term, then tap its definition

Match each electrical device with its correct function in a circuit.

① Terms — tap or drag

Ammeter

Voltmeter

Rheostat

Fuse

MCB

Switch

② Definitions — drop or tap here

Opens or closes the circuit — controls current flow

Variable resistor — controls current in circuit

Measures voltage — connected in parallel

Measures current — connected in series

Safety device — melts to break overloaded circuit

Modern resettable circuit breaker — replaces fuse

Experiment: Verify Ohm's Law

Aim: To verify Ohm's Law and study the relationship between current (I) and potential difference (V) for a metallic conductor.

Materials

Nichrome wire of known length and cross-section
Battery (6 V) or variable DC power supply
Rheostat (variable resistor)
Ammeter (0–3 A range)
Voltmeter (0–10 V range)
Connecting wires and switch
Graph paper and pencil

Procedure

Connect the circuit: Battery → Switch → Ammeter → Nichrome wire → Rheostat (in series). Connect voltmeter across the nichrome wire (in parallel).
Close the switch and adjust the rheostat to set the current to the lowest readable value.
Record the ammeter reading (I) and voltmeter reading (V).
Increase the rheostat setting to increase current. Record 6–8 pairs of V and I values.
Plot a graph of V (y-axis) vs I (x-axis) on graph paper.
Calculate R = V/I for each reading and check if it remains approximately constant.
Draw the best-fit straight line through the origin.

Observation

The graph of V vs I is a straight line passing through the origin. The ratio V/I remains approximately constant for all readings, equal to the resistance of the wire.

Conclusion

Since V/I = constant = R, and the V–I graph is a straight line through the origin, Ohm's Law is verified: V ∝ I at constant temperature. The slope of the V–I graph gives the resistance (R) of the conductor.

Experiment: Factors Affecting Resistance of a Wire

Aim: To study the dependence of resistance of a wire on its length, cross-sectional area, and material.

Materials

Wires of different materials (nichrome, copper, aluminium) — same length and area
Wires of same material (nichrome) — different lengths
Wires of same material and length — different cross-sectional areas (gauges)
Battery, ammeter, voltmeter, switch, connecting wires

Procedure

Set up the basic Ohm's Law circuit with ammeter in series and voltmeter in parallel.
Experiment 1 (Effect of Length): Connect nichrome wires of different lengths (20 cm, 40 cm, 60 cm). Record V and I; calculate R = V/I.
Experiment 2 (Effect of Area): Connect nichrome wires of same length but different gauges (areas). Record V and I; calculate R.
Experiment 3 (Effect of Material): Connect wires of copper, nichrome, and aluminium of same length and area. Compare R values.
Tabulate all observations and compare how R changes in each case.

Observation

R increases proportionally with length. R decreases as cross-sectional area increases. R depends on the type of material — nichrome has much higher R than copper for identical dimensions.

Conclusion

Resistance of a wire is directly proportional to its length (R ∝ L), inversely proportional to its cross-sectional area (R ∝ 1/A), and depends on the nature of its material (resistivity ρ). This confirms R = ρL/A.

Water Flow Analogy for Electric Circuit

Water System

Water pump (creates pressure difference)
Water pressure (drives water flow)
Flow rate of water (litres/second)
Narrow pipe (restricts flow)
Friction in pipe (opposes flow)
Water flowing in pipe
Parallel pipes (same pressure across each)

⇄

Electric Circuit

Battery / cell (creates potential difference)
Voltage / potential difference (drives current)
Electric current (Coulombs/second = Amperes)
Thin wire or high resistance (restricts current)
Resistance (opposes current flow)
Electrons drifting in wire
Parallel resistors (same voltage across each)

Just as water flows from high pressure to low pressure, electric current flows from high potential to low potential. The battery is the 'pump' that maintains this pressure difference continuously.

Test Your Understanding — Section 1: Basics

Q1 If 6 C of charge flows through a wire in 2 seconds, the electric current is:

A. 3 A

B. 12 A

C. 8 A

D. 0.33 A

I = Q/t = 6/2 = 3 A. Current = charge divided by time.

Q2 A charge of 4 C does 20 J of work while moving between two points. The potential difference is:

A. 80 V

B. 0.2 V

C. 5 V

D. 16 V

V = W/Q = 20/4 = 5 V. Potential difference = work done per unit charge.

Q3 A voltmeter is always connected in _______ with the component being measured.

A. Series

B. Parallel

C. Either

D. Neither

A voltmeter measures the potential difference (voltage) ACROSS a component, so it must be connected in PARALLEL. If connected in series, it would block most of the current due to its high resistance.

Q4 Which of the following does NOT affect the resistance of a metallic conductor?

A. Length of conductor

B. Colour of conductor

C. Temperature of conductor

D. Material of conductor

The colour of the conductor has no effect on its resistance. Resistance depends on length, cross-sectional area, material (resistivity), and temperature — but not colour.

Test Your Understanding — Section 2: Ohm's Law & Resistance

Q1 A 10 Ω and a 20 Ω resistor are connected in series across a 6 V battery. The current through the circuit is:

A. 0.6 A

B. 0.2 A

C. 1.0 A

D. 3.0 A

Series resistance = 10 + 20 = 30 Ω. I = V/R = 6/30 = 0.2 A.

Q2 Two 6 Ω resistors are connected in parallel. The equivalent resistance is:

A. 12 Ω

B. 6 Ω

C. 3 Ω

D. 1 Ω

For two equal resistors (R each) in parallel: Rₚ = R/2 = 6/2 = 3 Ω. Or using 1/Rₚ = 1/6 + 1/6 = 2/6 → Rₚ = 3 Ω.

Q3 If the length of a wire is doubled and its cross-section is halved, its resistance becomes:

A. Same

B. 2 times

C. 4 times

D. Half

R = ρL/A. New R = ρ(2L)/(A/2) = 4ρL/A = 4R. So resistance becomes 4 times.

Q4 Which material has the lowest resistivity and is the best conductor?

A. Copper

B. Nichrome

C. Silver

D. Tungsten

Silver has the lowest resistivity (~1.6 × 10⁻⁸ Ω·m) making it the best electrical conductor, but copper is used more practically due to its lower cost.

Q5 The V–I graph for an ohmic conductor is:

A. A curve

B. A straight line not passing through origin

C. A straight line through the origin

D. A parabola

For an ohmic conductor, V ∝ I (Ohm's Law), so the V–I graph is a straight line passing through the origin. The slope of this line gives the resistance R.

Test Your Understanding — Section 3: Power & Heating Effect

Q1 An electric heater of resistance 8 Ω draws 4 A current. Heat produced in 5 minutes is:

A. 38,400 J

B. 9,600 J

C. 160 J

D. 4,800 J

H = I²Rt = (4)² × 8 × (5 × 60) = 16 × 8 × 300 = 38,400 J.

Q2 A 1000 W geyser is used for 2 hours daily for 30 days. Units consumed and cost at ₹5/unit:

A. 30 units, ₹150

B. 60 units, ₹300

C. 6 units, ₹30

D. 600 units, ₹3000

Power = 1000 W = 1 kW. Energy = 1 kW × 2 h × 30 days = 60 kWh = 60 units. Cost = 60 × ₹5 = ₹300.

Q3 The filament of an electric bulb is made of tungsten because:

A. It has low resistivity

B. It has a very high melting point

C. It is a good conductor of heat

D. It is cheap and easily available

Tungsten has a very high melting point (3380°C), so it can be heated to white-hot temperatures to emit light without melting. Its high resistivity also means it generates sufficient heat/light.

Q4 If the current through a resistor is doubled, the heat produced in it becomes:

A. Double

B. Half

C. Four times

D. Same

H = I²Rt. If I becomes 2I, then H = (2I)²Rt = 4I²Rt = 4H. Heat becomes 4 times (this is why fuse protection is critical — small increases in current cause large increases in heat).

Summary: All Important Formulae

Quantity	Formula	Unit	Key Relation
Electric Current	I = Q / t	Ampere (A)	1 A = 1 C/s
Potential Difference	V = W / Q	Volt (V)	1 V = 1 J/C
Resistance (Ohm's Law)	R = V / I	Ohm (Ω)	1 Ω = 1 V/A
Resistivity	ρ = RA / L	Ω·m	Material property only
Resistance from ρ	R = ρL / A	Ohm (Ω)	R ∝ L; R ∝ 1/A
Series Resistance	Rₛ = R₁ + R₂ + R₃	Ohm (Ω)	Rₛ > max(R)
Parallel Resistance	1/Rₚ = 1/R₁ + 1/R₂	Ohm (Ω)	Rₚ < min(R)
Heat (Joule's Law)	H = I²Rt	Joule (J)	H = VIt = V²t/R
Electric Power	P = VI = I²R = V²/R	Watt (W)	P = H / t
Electrical Energy	E = Pt = VIt	Joule (J) / kWh	1 kWh = 3.6×10⁶ J

Common Doubts — Electricity

Why does resistance increase with temperature for metals?

As temperature rises, the ions in the metal lattice vibrate more vigorously. This increases the frequency and intensity of collisions between free electrons and lattice ions, making it harder for electrons to flow. Result: resistance increases. This is why the filament of a bulb has very high resistance when hot (glowing) compared to when cold.

Why are household appliances connected in parallel and not in series?

In parallel: (1) Each appliance gets full 220 V — it works at its rated voltage. (2) If one appliance fails, others continue working. (3) Each appliance can be switched on/off independently. In series, voltage would divide, appliances would not get full voltage, and failure of one would stop all others.

What is the difference between electric energy and electric power?

Power (P) is the RATE of energy consumption — how fast energy is used, measured in Watts (W). Energy (E) is the TOTAL amount of energy consumed over time — E = P × t, measured in Joules (J) or kWh. A 1000 W geyser uses more energy than a 100 W bulb in the same time because its power is 10× higher.

Why is it dangerous to touch an electric wire with wet hands?

Water (especially with dissolved salts) is a good conductor of electricity. Dry skin has high resistance (~100,000 Ω) which limits current flow. Wet skin drops resistance to as low as 1000 Ω, allowing much more current to flow through the body — enough to cause a fatal shock. This is why electrical safety rules prohibit handling electrical equipment with wet hands.

What is the difference between a fuse and an MCB?

A fuse is a thin wire that melts and permanently breaks the circuit during overcurrent — it must be replaced after it blows. An MCB (Miniature Circuit Breaker) is a mechanical switch that automatically trips (opens) during overcurrent and can be reset by simply pushing a button — no replacement needed. MCBs are safer, more reliable, and more convenient than fuses.

If two identical bulbs are connected first in series then in parallel to the same battery, in which case do they glow brighter?

Parallel connection — each bulb glows brighter. In parallel, each bulb gets the full battery voltage (V), so power = V²/R is maximum. In series, the voltage is halved (V/2 across each bulb), so power = (V/2)²/R = V²/4R — only one-quarter the power. Total power consumed is also higher in parallel, which is why parallel is used in homes.

What does the slope of a V–I graph represent?

The slope of the V–I graph (V on y-axis, I on x-axis) equals V/I = R — the resistance of the conductor. A steeper slope means higher resistance. For an ohmic conductor, this slope is constant (straight line). For a non-ohmic conductor (like a diode), the slope changes — meaning resistance is not constant.

Lightning carries about 1 billion volts but only lasts for milliseconds — the reason it kills is the massive current (up to 30,000 A), not just the voltage.

— National Geographic

The human body is a poor conductor — but only until it's wet. Dry skin resists ~100,000 Ω; wet skin drops this to ~1,000 Ω, making 'don't touch electricity with wet hands' a life-saving rule.

— Physics of Safety

If all the electrons in just 1 gram of copper could be moved, the resulting current would power the entire Earth's electricity needs for about 3,000 years.

— Conceptual Physics

The word 'electricity' comes from the Greek word 'elektron' meaning amber — because ancient Greeks discovered static electricity by rubbing amber cloth.

— Etymology

Chapter Summary — Electricity

Everything you need for the board exam, in one place.

Key Takeaways

Electric current I = Q/t; unit is Ampere (A); measured by ammeter in series.
Potential difference V = W/Q; unit is Volt (V); measured by voltmeter in parallel.
Ohm's Law: V = IR (for ohmic conductors at constant temperature).
Resistance R = ρL/A — depends on material, length, and area; not on colour or shape of cross-section.
Series: R_total = R₁+R₂+...; same I, voltage divides.
Parallel: 1/R_total = 1/R₁+1/R₂+...; same V, current divides.
Joule's Law: H = I²Rt = VIt = V²t/R — heat is proportional to I².
Electric Power P = VI = I²R = V²/R; unit is Watt (W).
Commercial energy unit: 1 kWh = 1 unit = 3.6 × 10⁶ J.
Household appliances in parallel — each gets 220 V, works independently.

Exam Tips

Always check: Ammeter → series; Voltmeter → parallel. Getting these swapped is a common 1-mark error.
For resistor problems: draw the circuit first, label series/parallel, then apply formulas.
For heating problems: convert time to seconds before using H = I²Rt.
For electricity bill: convert W to kW, then multiply by hours to get kWh.
V–I graph slope = R (resistance). I–V graph slope = 1/R (conductance).
If resistance doubles (R → 2R): for same V, current halves; for same I, heat doubles.
Resistivity is a material property — it doesn't change when you change length or area.

Current Voltage Resistance Ohm's Law Joule's Law Power Series Parallel Resistivity Class 10 CBSE Board Exam