Class 10 Science Notes Chapter 12 (Chapter 12) – Examplar Problems (English) Book

Detailed Notes with MCQs of Chapter 12, Electricity, from your NCERT Exemplar. This is a crucial chapter, not just for your board exams but also for various government exams where basic science is tested. We'll break down the key concepts thoroughly.

Chapter 12: Electricity - Detailed Notes for Competitive Exams

1. Electric Current and Circuit

• Electric Current (I): The rate of flow of electric charge (Q) through a conductor. Conventionally, the direction of current is taken as the direction of flow of positive charge (opposite to the flow of electrons).
  • Formula: I = Q / t
  • Where:
    • I = Current
    • Q = Net charge flowing
    • t = Time duration
  • Unit: Ampere (A). Defined as 1 Coulomb of charge flowing per second (1 A = 1 C/s).
  • Smaller Units: milliampere (mA = 10⁻³ A), microampere (µA = 10⁻⁶ A).
  • Measurement: Using an Ammeter, always connected in series in the circuit. An ideal ammeter has very low (ideally zero) resistance.
• Electric Charge (Q): Fundamental property of matter. Electrons carry negative charge (-1.6 x 10⁻¹⁹ C), protons carry positive charge (+1.6 x 10⁻¹⁹ C).
  • Formula: Q = n * e
  • Where:
    • n = number of electrons
    • e = charge on one electron (1.6 x 10⁻¹⁹ C)
  • Unit: Coulomb (C).
• Electric Circuit: A continuous and closed path along which an electric current can flow. Components include a source (cell/battery), conductor (wires), switch/key, and load (bulb/resistor).

2. Electric Potential and Potential Difference (Voltage)

• Electric Potential: The amount of work done in moving a unit positive charge from infinity to a specific point in an electric field.
• Potential Difference (V): The work done (W) to move a unit charge (Q) from one point to another in an electric circuit. It's what makes the charge flow.
  • Formula: V = W / Q
  • Unit: Volt (V). Defined as 1 Joule of work done per Coulomb of charge (1 V = 1 J/C).
  • Measurement: Using a Voltmeter, always connected in parallel across the points between which the potential difference is to be measured. An ideal voltmeter has very high (ideally infinite) resistance.
• Source: A cell or battery maintains the potential difference across the ends of a conductor.

3. Circuit Diagram and Symbols

• It's essential to know the standard symbols for components like: Cell, Battery, Connecting Wire, Wire Joint, Wire Crossing (no joint), Resistor (fixed), Variable Resistor (Rheostat), Ammeter, Voltmeter, Galvanometer, Open Switch, Closed Switch, Electric Bulb. (Refer to your NCERT book/Exemplar for the visual symbols).

4. Ohm's Law

• Statement: At a constant temperature, the current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends.
  • Mathematically: V ∝ I
  • Formula: V = IR
  • Where R is the constant of proportionality called Resistance.
• 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). The slope of the I-V graph gives the reciprocal of resistance (Conductance).
• Resistance (R): The property of a conductor to resist the flow of charges through it.
  • Unit: Ohm (Ω). Defined as 1 Volt per Ampere (1 Ω = 1 V/A).

5. Factors Affecting Resistance

The resistance of a conductor depends on:

• Length (l): R ∝ l (Longer wire, more resistance)
• Area of Cross-section (A): R ∝ 1/A (Thicker wire, less resistance)
• Nature of Material: Different materials offer different resistance. This is quantified by resistivity.
• Temperature: Resistance generally increases with an increase in temperature for most conductors (like metals). For alloys, the change is less significant. For semiconductors, resistance decreases with increasing temperature.

6. Resistivity (ρ) (Specific Resistance)

• From the factors above, R ∝ l/A or R = ρ (l/A)
• Definition: Resistivity is the resistance offered by a cube of the material of side 1 metre when current flows perpendicular to its opposite faces. It's an intrinsic property of the material.
  • Formula: ρ = R * A / l
  • Unit: Ohm-meter (Ω m).
• Dependence: Resistivity depends on the nature of the material and temperature. It does not depend on the length or thickness (dimensions) of the conductor.
• Classification based on Resistivity:
  • Conductors (Metals, Alloys): Low resistivity (e.g., Silver, Copper, Aluminium). Alloys (like Nichrome, Manganin) have higher resistivity than constituent metals and are used in heating devices and standard resistors.
  • Insulators (Rubber, Glass, Plastic): Very high resistivity.
  • Semiconductors (Silicon, Germanium): Resistivity between conductors and insulators.

7. Resistance of a System of Resistors

• Resistors in Series:
  • Connected end-to-end, forming a single path for current.
  • Current: Same through each resistor (I = I₁ = I₂ = ...).
  • Voltage: Total voltage across the combination is the sum of voltages across individual resistors (V = V₁ + V₂ + ...).
  • Equivalent Resistance (Rs): Rs = R₁ + R₂ + R₃ + ...
  • Key Point: Equivalent resistance in series is always greater than the largest individual resistance.
• Resistors in Parallel:
  • Connected between the same two points, providing multiple paths for current.
  • Voltage: Same across each resistor (V = V₁ = V₂ = ...).
  • Current: Total current is the sum of currents through individual branches (I = I₁ + I₂ + ...).
  • Equivalent Resistance (Rp): 1/Rp = 1/R₁ + 1/R₂ + 1/R₃ + ...
  • Key Point: Equivalent resistance in parallel is always smaller than the smallest individual resistance.
  • Special Case (Two Resistors): Rp = (R₁ * R₂) / (R₁ + R₂)

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

• When current flows through a purely resistive conductor, electrical energy is dissipated entirely in the form of heat.
• Joule's Law of Heating: 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
• Unit: Joule (J).
• Applications: Electric heater, electric iron, electric bulb (filament heating), electric fuse (melts and breaks circuit on overheating due to excess current).
• Electric Fuse: A safety device containing a wire (usually an alloy of lead and tin) with a low melting point. It's always connected in series with the live wire. It protects circuits and appliances by stopping the flow of unduly high electric current.

9. Electric Power (P)

• Definition: The rate at which electric energy is consumed or dissipated in an electric circuit.
  • Formula: P = W / t (Work done or Energy consumed per unit time)
  • Since W = VIt, we get P = VIt / t = VI
  • Other forms (using V=IR): P = I²R and P = V²/R
• Unit: Watt (W). Defined as 1 Joule per second (1 W = 1 J/s). Also, 1 Watt = 1 Volt x 1 Ampere (1 W = 1 VA).
• Larger Units: kilowatt (kW = 1000 W), megawatt (MW = 10⁶ W).
• Commercial Unit of Energy: kilowatt-hour (kWh), often called a 'unit'.
  • 1 kWh = 1 kilowatt * 1 hour = 1000 W * 3600 s = 3.6 x 10⁶ Ws = 3.6 x 10⁶ J
  • This is the unit used in electricity bills.

10. Calculating Energy Consumption

• Energy (E) = Power (P) x Time (t)
• If Power is in kW and Time is in hours, Energy is in kWh.
• Example: A 100 W bulb used for 5 hours consumes Energy = (100/1000) kW * 5 h = 0.1 kW * 5 h = 0.5 kWh.

Multiple Choice Questions (MCQs)

1. A piece of wire of resistance R is cut into five equal parts. These parts are then connected in parallel. If the equivalent resistance of this combination is R', then the ratio R/R' is:
   a) 1/25
   b) 1/5
   c) 5
   d) 25

2. Which of the following terms does not represent electrical power in a circuit?
   a) I²R
   b) IR²
   c) VI
   d) V²/R

3. An electric bulb is rated 220 V and 100 W. When it is operated on 110 V, the power consumed will be:
   a) 100 W
   b) 75 W
   c) 50 W
   d) 25 W

4. Two conducting wires of the same material and of equal lengths and equal diameters are first connected in series and then parallel in a circuit across the same potential difference. The ratio of heat produced in series and parallel combinations would be:
   a) 1:2
   b) 2:1
   c) 1:4
   d) 4:1

5. What is the maximum resistance which can be made using five resistors each of 1/5 Ω?
   a) 1/5 Ω
   b) 10 Ω
   c) 5 Ω
   d) 1 Ω

6. The resistivity of a material depends on:
   a) Length of the conductor
   b) Area of cross-section of the conductor
   c) Temperature
   d) Both length and area of cross-section

7. A student carries out an experiment and plots the V-I graph of three samples of nichrome wire with resistances R₁, R₂, and R₃ respectively. Which of the following is true? (Assume V is on y-axis, I on x-axis)
   a) R₁ = R₂ = R₃
   b) R₁ > R₂ > R₃
   c) R₃ > R₂ > R₁
   d) Cannot be determined without knowing the slopes

8. If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be:
   a) 100 %
   b) 200 %
   c) 300 %
   d) 400 %

9. An electric kettle consumes 1 kW of electric power when operated at 220 V. A fuse wire of what rating must be used for it?
   a) 1 A
   b) 2 A
   c) 4 A
   d) 5 A

10. Unit of electric charge is:
    a) Ampere (A)
    b) Volt (V)
    c) Coulomb (C)
    d) Ohm (Ω)

Answer Key for MCQs:

1. d) 25
2. b) IR²
3. d) 25 W
4. c) 1:4
5. d) 1 Ω
6. c) Temperature
7. (Assuming R1 has the steepest slope, R3 the least steep) b) R₁ > R₂ > R₃ (Since Slope = R)
8. c) 300 %
9. d) 5 A
10. c) Coulomb (C)

Make sure you understand the reasoning behind each MCQ answer, especially the calculations involved in questions 1, 3, 4, 5, 8, and 9. Revise these concepts regularly. Good luck!