From powering our smartphones and lighting our homes to driving high-speed trains and industrial machinery, electricity is the backbone of modern technological civilization. In CBSE Class 10 Physics Chapter 12 (Electricity), we study the fundamental physical quantities governing electric circuits: charge, current, voltage, resistance, electrical power, and heating effects.
This guide provides a comprehensive walkthrough of Ohm’s law, resistivity, series and parallel resistor networks, Joule’s law of heating, electrical power formulas, commercial energy calculations, and five step-by-step solved board exam numericals.
V = W / Q
A = πr²
H = (V²/R)t
P = I²R = V²/R
- 1. Electric Current & Potential Difference
- 2. Ohm's Law & Circuit Diagram Symbols
- 3. Factors Affecting Resistance & Resistivity (ρ)
- 4. Series vs Parallel Combination of Resistors
- 5. Heating Effect of Electric Current (Joule's Law)
- 6. Practical Applications (Fuse, Bulb, Electric Heater)
- 7. Electric Power & Commercial Energy Unit (kWh)
- 8. Solved Board Exam Numericals
- 9. Frequently Asked Questions (FAQ)
1. Electric Current & Potential Difference
• Formula: I = Q / t (where Q = total charge in Coulombs, t = time in seconds).
• SI Unit: Ampere (A). 1 Ampere = 1 Coulomb / 1 Second.
• Charge of an electron: e = 1.6 × 10⁻¹⁹ C. Total charge Q = n × e (n = number of electrons). 1 Coulomb = 6.25 × 10¹⁸ electrons.
• Measuring Instrument: Ammeter (always connected in SERIES in a circuit; has very low resistance).
• Formula: V = W / Q (where W = work done in Joules, Q = charge in Coulombs).
• SI Unit: Volt (V). 1 Volt = 1 Joule / 1 Coulomb.
• Cause of Current: Potential difference created by a cell/battery maintains current flow from high potential (+) to low potential (−).
• Measuring Instrument: Voltmeter (always connected in PARALLEL across the component; has very high resistance).
2. Ohm's Law & Circuit Diagram Symbols
• V-I Graph: A straight line passing through the origin. The slope of the V-I graph represents the Resistance (R) of the conductor.
• SI Unit of Resistance: Ohm (Ω). 1 Ohm = 1 Volt / 1 Ampere.
3. Factors Affecting Resistance & Resistivity (ρ)
Resistance is the property of a conductor to oppose the flow of electric current through it.
Factors Affecting Resistance:
- Length of Conductor (L): Resistance is directly proportional to length → R ∝ L. (Doubling length doubles resistance).
- Area of Cross-Section (A): Resistance is inversely proportional to area → R ∝ 1/A. (Thicker wire has lower resistance).
- Nature of Material (ρ): Represented by Electrical Resistivity.
- Temperature: Resistance of pure metals increases with temperature.
• SI Unit of Resistivity: Ohm-meter (Ω·m).
• Conductors: Low resistivity (~10⁻⁸ to 10⁻⁶ Ω·m). E.g., Silver (1.6 × 10⁻⁸ Ω·m), Copper, Aluminium.
• Alloys: Higher resistivity than constituent metals (~10⁻⁶ Ω·m). E.g., Nichrome (Ni+Cr+Mn+Fe), Constantan, Manganin. Alloys do NOT oxidize (burn) easily at high temperatures → used in heating elements!
4. Series vs Parallel Combination of Resistors
| Feature | Series Combination | Parallel Combination |
|---|---|---|
| Circuit Diagram Layout | Resistors connected end-to-end in a single loop | Resistors connected across common positive and negative terminals |
| Equivalent Resistance | Rᵲ = R₁ + R₂ + R₃ (Increases total resistance) | 1/Rᵖ = 1/R₁ + 1/R₂ + 1/R₃ (Decreases total resistance) |
| Electric Current (I) | SAME current flows through all resistors (I = I₁ = I₂ = I₃) | Current divides among branches (I = I₁ + I₂ + I₃) |
| Potential Difference (V) | Voltage divides across resistors (V = V₁ + V₂ + V₃) | SAME voltage across all resistors (V = V₁ = V₂ = V₃) |
| If One Component Fails | Entire circuit breaks; all appliances stop working | Other branches continue working independently |
| Domestic Appliance Application | NOT suitable for house wiring (used in decorative fairy lights) | IDEAL for domestic house wiring (independent switches) |
5. Heating Effect of Electric Current (Joule's Law)
When an electric current flows through a purely resistive conductor, electrical energy is converted into heat energy. This is known as the heating effect of electric current.
1. Directly proportional to the square of current (I²) for a given resistance.
2. Directly proportional to resistance (R) for a given current.
3. Directly proportional to the time (t) for which current flows.
6. Practical Applications (Fuse, Bulb, Electric Heater)
- Electric Heating Appliances: Electric iron, toaster, water heater, room heater use heating elements made of Nichrome alloy because of its high resistivity and high melting point (does not oxidize/burn at red-hot heat).
- Electric Bulb: Uses a thin Tungsten filament (melting point = 3380°C, extremely high!). Bulb is filled with chemically inactive gases like Argon or Nitrogen to prolong filament life. Most electrical energy is lost as heat; only a small fraction is emitted as light.
- Electric Fuse (Safety Device): Connected in SERIES with the live wire. Consists of a thin wire of lead-tin alloy having a low melting point. If current exceeds safe limit, Joule's heat melts the fuse wire, breaking the circuit and preventing damage to expensive appliances and fires.
7. Electric Power & Commercial Energy Unit (kWh)
• SI Unit: Watt (W). 1 Watt = 1 Joule / 1 Second = 1 Volt × 1 Ampere.
• 1 Kilowatt (kW) = 1000 W | 1 Megawatt (MW) = 10⁶ W.
1 kWh = 1 kW × 1 Hour
= 1000 Watts × 3600 Seconds
= 1000 (J/s) × 3600 s = 3,600,000 Joules = 3.6 × 10⁶ J.
Electricity utility meters measure consumption in Kilowatt-hours (kWh), commonly called "Units".
8. Solved Board Exam Numericals
Ohm's Law: I = V / R = 220 / 1200 = 0.18 A.
(b) For Heater: V = 220 V, R = 100 Ω.
I = V / R = 220 / 100 = 2.2 A.
Area A = πr² = 3.14 × (0.25 × 10⁻³)² = 3.14 × 0.0625 × 10⁻⁶ = 1.9625 × 10⁻⁷ m².
Resistivity ρ = 1.6 × 10⁻⁸ Ω·m, Resistance R = 10 Ω.
Formula: R = ρL / A → L = (R × A) / ρ
L = (10 × 1.9625 × 10⁻⁷) / (1.6 × 10⁻⁸) = 1.9625 × 10⁻⁶ / 1.6 × 10⁻⁸
L = 122.7 m.
(a) Parallel Resistance: 1/Rᵖ = 1/5 + 1/10 + 1/30 = (6 + 3 + 1) / 30 = 10 / 30 = 1/3.
Rᵖ = 3 Ω.
(b) Total Current: I = V / Rᵖ = 12 / 3 = 4 A.
Resistance R = 4 Ω.
Formula: P = V² / R → V² = P × R
V² = 100 × 4 = 400 → V = √400 = 20 V.
Total time in 30 days t = 8 hours/day × 30 days = 240 hours.
Energy consumed E = P × t = 0.4 kW × 240 h = 96 kWh (Units).
Cost = 96 kWh × ₹ 3.00 = ₹ 288.00.
Explore Related CBSE Class 9 & 10 Science Guides
9. Frequently Asked Questions (FAQ)
Ohm’s law states that the electric current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends, provided its temperature remains constant.
Formula: V = IR (where R is Resistance).
The V-I graph is a straight line passing through the origin, and its slope represents Resistance R.
Parallel combination is preferred in domestic circuits because:
(1) Each appliance gets the same full line voltage (220 V).
(2) Each appliance has its own independent switch.
(3) If one appliance fails or breaks, other appliances continue working independently.
(4) Total equivalent resistance decreases, reducing energy loss.
Joule’s law of heating states that heat produced in a resistor is directly proportional to the square of current, resistance, and time: H = I²Rt.
Applications: Electric iron, electric heater, toaster, electric fuse (safety device with low melting point), and electric bulb (tungsten filament).
The commercial unit of electrical energy is the Kilowatt-hour (kWh), commonly called a "Unit".
1 kWh = 3.6 × 10⁶ Joules (3.6 million Joules).
Derivation: 1 kWh = 1000 W × 3600 s = 3,600,000 J.
Tungsten is used for bulb filaments because it has an extremely high melting point (3380°C) and high resistivity, allowing it to glow white-hot without melting.
Nichrome (alloy of Ni, Cr, Mn, Fe) is used for heating elements because it has high resistivity and does NOT oxidize (burn) even at very high red-hot temperatures.
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