Class 10 Notes

Class 10 Science Notes Chapter 12 (Electricity) – Science Book

Philoid

Philoid

— 6 min read

Science
Alright class, let's get straight into Chapter 12: Electricity. This is a fundamental chapter, not just for your Class 10 understanding, but also forms the basis for many questions in competitive government exams. Pay close attention to the definitions, laws, formulas, and applications.

Chapter 12: Electricity - Detailed Notes for Government Exam Preparation

1. Electric Current and Circuit

  • Electric Charge (Q): A fundamental property of matter. Like charges repel, unlike charges attract.
    • SI Unit: Coulomb (C)
    • Charge on one electron = -1.6 x 10⁻¹⁹ C
    • Charge on one proton = +1.6 x 10⁻¹⁹ C
    • Quantization of Charge: Q = ne (where n is an integer, e is the charge of an electron)
  • Electric Current (I): The rate of flow of electric charge through a conductor.
    • Formula: I = Q / t (where Q is the charge flowing in time t)
    • SI Unit: Ampere (A)
    • Definition of 1 Ampere: 1 Ampere is constituted by the flow of 1 Coulomb of charge per second (1 A = 1 C/s).
    • Direction: Conventionally, the direction of current is taken as the direction of flow of positive charge (opposite to the direction of flow of electrons).
    • Measurement: Measured by an Ammeter, always connected in series in the circuit. An ideal ammeter has very low resistance.
  • Electric Circuit: A continuous and closed path along which an electric current can flow. A simple circuit consists of a source (cell/battery), a load (bulb/resistor), connecting wires, and a switch (key).

2. Electric Potential and Potential Difference

  • Electric Potential: The electric potential at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point.
  • Potential Difference (V): The work done to move a unit charge from one point to another in an electric field. It's what makes the charge flow in a conductor.
    • Formula: V = W / Q (where W is the work done to move charge Q)
    • SI Unit: Volt (V)
    • Definition of 1 Volt: The potential difference between two points is said to be 1 Volt if 1 Joule of work is done in moving 1 Coulomb of charge from one point to the other (1 V = 1 J/C).
    • Measurement: Measured by a Voltmeter, always connected in parallel across the points between which the potential difference is to be measured. An ideal voltmeter has very high resistance.

3. Circuit Diagram and Symbols

  • Standard symbols are used to represent components in a circuit diagram for clarity and uniformity. Key symbols include:
    • Electric Cell: +|−
    • Battery (combination of cells): +|−|−
    • Plug Key (open): ( )
    • Plug Key (closed): (.)
    • Wire Joint: • (at the junction)
    • Wires Crossing (no connection): ──┼── (one wire jumps over)
    • Electric Bulb: (⊗) or a loop symbol
    • Resistor: zigzag line
    • Variable Resistance (Rheostat): zigzag line with arrow across or through it
    • Ammeter: Ⓐ (with + and - terminals)
    • Voltmeter: ⓥ (with + and - terminals)

4. Ohm's Law

  • Statement: At a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends.
  • Mathematical Expression: V ∝ I
    • V = IR (where R is the constant of proportionality called Resistance)
  • Resistance (R): The property of a conductor to resist the flow of charges through it.
    • Formula: R = V / I
    • SI Unit: Ohm (Ω)
    • Definition of 1 Ohm: A conductor has a resistance of 1 Ohm if a potential difference of 1 Volt across its ends causes a current of 1 Ampere to flow through it (1 Ω = 1 V/A).
  • V-I Graph: For an ohmic conductor (obeys Ohm's Law), the graph between V (on y-axis) and I (on x-axis) is a straight line passing through the origin. The slope of the V-I graph gives the resistance (Slope = V/I = R).

5. Factors Affecting Resistance of a Conductor

  • The resistance (R) of a conductor depends on:
    • Length (l): R ∝ l (Resistance increases with length)
    • Area of Cross-section (A): R ∝ 1/A (Resistance decreases with increasing thickness/area)
    • Nature of the Material: Different materials offer different resistance.
    • Temperature: Resistance generally increases with increasing temperature for most conductors.
  • Combining the factors: R ∝ l/A
    • R = ρ (l/A)
  • Resistivity (ρ) or Specific Resistance: It is the constant of proportionality, characteristic of the material of the conductor.
    • Definition: Resistivity is numerically equal to the resistance of a conductor of unit length and unit cross-sectional area.
    • SI Unit: Ohm-meter (Ωm)
    • Significance:
      • Conductors (metals like Cu, Al) have very low resistivity (10⁻⁸ to 10⁻⁶ Ωm).
      • Insulators (rubber, glass, plastic) have very high resistivity (10¹² to 10¹⁷ Ωm).
      • Semiconductors (Si, Ge) have intermediate resistivity.
      • Alloys generally have higher resistivity than their constituent metals and do not oxidize (burn) readily at high temperatures. Hence, they are used in heating devices (e.g., Nichrome in heaters, Manganin/Constantan in standard resistors).

6. Resistance of a System of Resistors

  • Resistors in Series:
    • Connection: End-to-end, forming a single path for current.
    • Current: Same current flows through each resistor (I_total = I₁ = I₂ = ...).
    • Voltage: Total potential difference across the combination is the sum of potential differences across individual resistors (V_total = V₁ + V₂ + ...).
    • Equivalent Resistance (Rs): The single resistance that can replace the combination while drawing the same current under the same voltage.
      • Formula: Rs = R₁ + R₂ + R₃ + ...
      • Note: The equivalent resistance in series is always greater than the largest individual resistance.
    • Disadvantage: If one component fails, the circuit breaks, and none work.
  • Resistors in Parallel:
    • Connection: Connected between the same two points, providing multiple paths for current.
    • Voltage: Potential difference across each resistor is the same and equal to the total potential difference (V_total = V₁ = V₂ = ...).
    • Current: Total current is the sum of currents through individual resistors (I_total = I₁ + I₂ + ...).
    • Equivalent Resistance (Rp):
      • Formula: 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + ...
      • Note: The equivalent resistance in parallel is always less than the smallest individual resistance.
    • Advantage: If one path/component fails, others continue to work. Used in household wiring.

7. Heating Effect of Electric Current (Joule's Law of Heating)

  • When current flows through a purely resistive conductor, electrical energy is dissipated entirely in the form of heat. This is the heating effect.
  • Joule's Law: The heat (H) produced in a resistor is:
    • Directly proportional to the square of the current (H ∝ I²)
    • Directly proportional to the resistance (H ∝ R)
    • Directly proportional to the time for which current flows (H ∝ t)
  • Formula: H = I²Rt
  • Other forms (using V=IR): H = VIt and H = (V²/R)t
  • SI Unit of Heat Energy: Joule (J)
  • Practical Applications:
    • Electric Heater, Iron, Toaster: Use heating elements made of alloys like Nichrome (high resistivity, high melting point).
    • Electric Bulb: Filament made of Tungsten (very high melting point ≈ 3380°C, high resistivity) glows when heated. Filled with inert gases (Nitrogen, Argon) to prolong filament life. Most energy is wasted as heat, only a small part is light.
    • Electric Fuse: A safety device connected in series with the mains supply or appliance. Made of a wire/alloy (like tin-lead or copper-tin) with an appropriate low melting point. If current exceeds a safe limit, the fuse wire melts, breaks the circuit, and prevents damage to appliances and wiring due to overheating.

8. Electric Power (P)

  • Definition: The rate at which electric energy is consumed or dissipated in an electric circuit.
  • Formula: P = W / t
    • Since W = VQ and Q = It, W = VIt.
    • Therefore, P = VIt / t => P = VI
  • Other forms (using V=IR): P = I²R and P = V²/R
  • SI Unit: Watt (W)
  • Definition of 1 Watt: Power consumed when 1 Ampere of current flows at a potential difference of 1 Volt (1 W = 1 V A).
  • Commercial Unit of Electrical Energy: kilowatt-hour (kWh), commonly known as a 'unit'.
    • 1 kWh is the energy consumed when a device of 1 kilowatt power operates for 1 hour.
    • Relation: 1 kWh = 1000 Watt x 3600 seconds = 3.6 x 10⁶ Watt-second = 3.6 x 10⁶ Joules (since 1 J = 1 Ws).
  • Calculating Energy Cost: Cost = Energy consumed in kWh × Rate per kWh.

Multiple Choice Questions (MCQs)

  1. The SI unit of electric potential difference is:
    a) Ampere (A)
    b) Ohm (Ω)
    c) Volt (V)
    d) Coulomb (C)

  2. According to Ohm's law, which relationship is correct?
    a) V ∝ R (I constant)
    b) I ∝ R (V constant)
    c) V ∝ I (R constant)
    d) R ∝ I (V constant)

  3. Resistivity of a metallic conductor depends on:
    a) Its length
    b) Its thickness (area of cross-section)
    c) The nature of its material
    d) Both length and thickness

  4. Three resistors of 2 Ω, 3 Ω, and 5 Ω are connected in series. The equivalent resistance of the combination is:
    a) 10 Ω
    b) (1/2 + 1/3 + 1/5) Ω
    c) Less than 2 Ω
    d) 30/31 Ω

  5. When resistors are connected in parallel:
    a) The current through each resistor is the same.
    b) The potential difference across each resistor is the same.
    c) The equivalent resistance is greater than the largest individual resistance.
    d) The total current is equal to the current through one resistor.

  6. Joule's law of heating states that the heat produced in a resistor is proportional to:
    a) I, R, t
    b) I², R, t
    c) V, I, t
    d) V², R, t

  7. Which of the following is NOT a correct formula for electric power (P)?
    a) P = VI
    b) P = I²R
    c) P = V²/R
    d) P = IR²/V

  8. The material used for making the filament of an electric bulb is:
    a) Copper
    b) Nichrome
    c) Tungsten
    d) Aluminium

  9. The commercial unit of electrical energy is:
    a) Joule (J)
    b) Watt (W)
    c) kilowatt-hour (kWh)
    d) Volt-Ampere (VA)

  10. If the length of a cylindrical wire is doubled and its radius is halved, its resistance will become:
    a) Half
    b) Double
    c) 4 times
    d) 8 times

Answer Key:

  1. c) Volt (V)
  2. c) V ∝ I (R constant)
  3. c) The nature of its material
  4. a) 10 Ω (Rs = 2 + 3 + 5)
  5. b) The potential difference across each resistor is the same.
  6. b) I², R, t
  7. d) P = IR²/V
  8. c) Tungsten
  9. c) kilowatt-hour (kWh)
  10. d) 8 times (R = ρl/A = ρl/(πr²). New R' = ρ(2l)/(π(r/2)²) = ρ(2l)/(πr²/4) = 8 * (ρl/πr²) = 8R)

Make sure you understand these concepts thoroughly. Practice numerical problems based on Ohm's law, resistance combinations, heating effect, and electric power. Good luck with your preparation!

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