Electricity

24. Case Study: A 12 V battery is connected to three resistors of 4 ohms, 6 ohms, and 12 ohms in parallel. Calculate the total resistance of the circuit and the total current flowing through the circuit.

• Answer:
  • For resistors in parallel, the total resistance (R_total) is given by:
    1/R_total = 1/R1 + 1/R2 + 1/R3
    1/R_total = 1/4 + 1/6 + 1/12
    1/R_total = 3/12 + 2/12 + 1/12
    1/R_total = 6/12 = 1/2
    R_total = 2 ohms.
  • The total current (I) can be calculated using Ohm’s law: I = V / R_total = 12 V / 2 ohms = 6 A.

25. Case Study: A wire of resistance 20 ohms is cut into two equal parts. These parts are then connected in parallel. What is the resistance of the combination?

• Answer:
  • When the wire is cut into two equal parts, the resistance of each part becomes 10 ohms.
  • For resistors in parallel:
    1/R_total = 1/R1 + 1/R2
    1/R_total = 1/10 + 1/10
    1/R_total = 2/10 = 1/5
    R_total = 5 ohms.

Higher Order Thinking Skills (HOTS) Questions

26. Explain why a thick copper wire has less resistance compared to a thin copper wire of the same length.

• Answer: The resistance of a wire is inversely proportional to its cross-sectional area. A thick wire has a larger cross-sectional area than a thin wire, resulting in lower resistance.

27. Why do electrical appliances with high power ratings use thicker wires?

• Answer: Appliances with high power ratings require more current. Thicker wires have lower resistance, allowing more current to flow without overheating the wire.

28. What happens to the brightness of a bulb if it is connected in series with another bulb of the same rating?

• Answer: When bulbs are connected in series, the total resistance increases, reducing the current through each bulb. As a result, both bulbs will glow dimmer compared to when they are connected individually.

29. How does the resistance of a conductor change if its temperature increases?

• Answer: The resistance of most conductors increases with an increase in temperature due to the increase in the vibration of atoms, which impedes the flow of electrons.

30. Why are alloys used in the heating elements of electrical devices rather than pure metals?

• Answer: Alloys have higher resistivity and do not oxidize or burn easily at high temperatures, making them suitable for use in heating elements.

True/False Questions

31. The current in a series circuit is the same at all points.
    Answer: True
32. The total resistance in a parallel circuit is always less than the smallest individual resistance.
    Answer: True
33. Ohm’s law is applicable to all types of conductors.
    Answer: False (Ohm’s law is applicable to only ohmic conductors, where the resistance remains constant with changes in voltage and current.)
34. A fuse wire is usually made of a material with a high melting point.
    Answer: False (A fuse wire is made of a material with a low melting point, so it melts easily when the current exceeds a certain limit.)
35. The resistance of a wire is directly proportional to its length and inversely proportional to its area of cross-section.
    Answer: True

Application-Based Questions

36. Why is it not advisable to connect a 100 W bulb and a 60 W bulb in series?

• Answer: In a series connection, both bulbs will share the same current, but the 100 W bulb, having a lower resistance, will not glow as brightly as it should. The 60 W bulb, with higher resistance, will restrict the current, reducing the brightness of both bulbs.

37. Explain why it is dangerous to replace a fuse with a wire of low resistance.

• Answer: A wire of low resistance will not melt easily even if the current exceeds the safe limit, leading to overheating and potential damage or fire in the circuit.

38. Why does the cord of an electric heater not become hot while the heating element does?

• Answer: The cord is made of materials with low resistance, allowing current to pass through without generating significant heat, whereas the heating element has high resistance, generating heat when current flows through it.

39. Why do electric transmission lines use high voltages?

• Answer: High voltages are used in transmission lines to reduce current and, consequently, minimize energy losses due to the heating effect (I²R losses) in the wires.

40. Why is a parallel circuit arrangement used in domestic wiring instead of a series circuit?

• Answer: A parallel circuit ensures that each appliance receives the full voltage of the supply and allows independent operation. If one appliance fails, others continue to operate.

Numerical Problems

41. Calculate the resistance of a wire if a current of 2 A flows through it when connected to a 12 V battery.

• Answer: Resistance (R) = Voltage (V) / Current (I)
  R = 12 V / 2 A = 6 ohms

42. A heater uses 5 A of current when connected to a 220 V source. Calculate the power consumed by the heater.

• Answer: Power (P) = Voltage (V) * Current (I)
  P = 220 V * 5 A = 1100 W

43. If a resistor of 10 ohms is connected to a 12 V battery, what is the power dissipated by the resistor?

• Answer: Power (P) = V² / R
  P = (12 * 12) / 10 = 144 / 10 = 14.4 W

44. Find the energy consumed by a 100 W bulb in 2 hours.

• Answer: Energy (E) = Power (P) * Time (T)
  E = 100 W * 2 hours = 200 watt-hours or 0.2 kWh

45. If a 1000 W appliance runs for 3 hours daily, calculate the monthly electricity consumption in kWh.

• Answer: Daily consumption = 1000 W * 3 hours = 3000 watt-hours or 3 kWh
  Monthly consumption = 3 kWh * 30 days = 90 kWh

Matching Questions

46. Match the unit with the corresponding quantity:
    • (a) Volt – (i) Resistance
    • (b) Ampere – (ii) Power
    • (c) Ohm – (iii) Voltage
    • (d) Watt – (iv) Current
      Answer: (a) – iii, (b) – iv, (c) – i, (d) – ii
47. Match the component with its symbol:
    • (a) Resistor – (i)
    • (b) Voltmeter – (ii)
    • (c) Ammeter – (iii)
    • (d) Cell – (iv)
      Answer: (a) – i, (b) – ii, (c) – iii, (d) – iv

Long Answer Questions

48. Describe the advantages of using parallel circuits in domestic wiring.

• Answer: Parallel circuits have several advantages:
  • Each appliance receives the full voltage supply, ensuring optimal performance.
  • Appliances can operate independently; if one fails, others continue to work.
  • It allows for different currents to flow through different appliances, depending on their resistance, without affecting others.

49. Explain the heating effect of electric current and its practical applications.

• Answer: The heating effect of electric current occurs when electric energy is converted into heat as current flows through a resistor. The amount of heat generated is given by the formula H = I²Rt. This effect is utilized in devices like electric heaters, irons, and toasters. It is also used in fuses, where excess heat due to high current melts the fuse, breaking the circuit and preventing damage.

50. Discuss the role of resistors in an electric circuit and how they are used to control the flow of current.

• Answer: Resistors are components that resist the flow of electric current, helping to control and manage the amount of current flowing through a circuit. They are used to divide voltage, limit current, and protect sensitive components by reducing the amount of current that can pass through the circuit.

True/False Questions (Continued)

51. Electric current flows from the positive terminal to the negative terminal of a battery.
    Answer: True
52. The total resistance in a series circuit is always less than the smallest individual resistance.
    Answer: False (The total resistance is the sum of all individual resistances.)
53. The SI unit of resistivity is ohm-meter.
    Answer: True
54. Electric power is defined as the rate at which electrical energy is converted into another form of energy.
    Answer: True
55. A rheostat is used to measure the potential difference across a resistor.
    Answer: False (A rheostat is used to vary the resistance in a circuit, not to measure potential difference.)

Numerical Problems (Continued)

56. A circuit has two resistors of 3 ohms and 6 ohms connected in series with a 9 V battery. Calculate the current flowing through the circuit.

• Answer: Total resistance (R_total) = 3 + 6 = 9 ohms
  Current (I) = Voltage (V) / Resistance (R) = 9 V / 9 ohms = 1 A

57. Calculate the equivalent resistance of two resistors, 4 ohms and 12 ohms, connected in parallel.

• Answer: 1/R_total = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3
  R_total = 3 ohms

58. An electric kettle has a power rating of 1500 W and is used for 30 minutes. Calculate the energy consumed in kilowatt-hours.

• Answer: Power (P) = 1500 W = 1.5 kW
  Time (T) = 30 minutes = 0.5 hours
  Energy (E) = P * T = 1.5 kW * 0.5 hours = 0.75 kWh

59. If the resistance of a conductor is 15 ohms and the current flowing through it is 2 A, calculate the voltage across the conductor.

• Answer: Voltage (V) = Current (I) * Resistance (R)
  V = 2 A * 15 ohms = 30 V

60. A 100 W bulb is used for 10 hours daily. Calculate the monthly electricity consumption in kilowatt-hours.

• Answer: Daily consumption = 100 W * 10 hours = 1000 watt-hours or 1 kWh
  Monthly consumption = 1 kWh * 30 days = 30 kWh

Fill in the Blanks

61. The flow of electric current is measured in ______.

• Answer: amperes

62. The resistance of a conductor depends on its ______, ______, and the material it is made of.

• Answer: length, cross-sectional area

63. In a parallel circuit, the ______ is the same across all components.

• Answer: voltage

64. The SI unit of power is ______.

• Answer: watt

65. In a series circuit, the total resistance is the ______ of the individual resistances.

• Answer: sum

Conceptual Questions

66. Explain why resistors in parallel have a lower equivalent resistance than any individual resistor.

• Answer: In a parallel circuit, each resistor provides an additional path for the current to flow, which decreases the overall resistance. The more resistors in parallel, the more paths available, and the lower the total resistance.

67. Describe the role of a voltmeter in an electric circuit.

• Answer: A voltmeter measures the potential difference (voltage) across two points in an electric circuit. It is always connected in parallel with the component whose voltage is to be measured.

68. Why is it important to connect an ammeter in series in a circuit?

• Answer: An ammeter measures the current flowing through a circuit. It must be connected in series so that all the current in the circuit passes through it, allowing for an accurate measurement.

69. What would happen if a fuse of higher rating is used in a circuit?

• Answer: If a fuse with a higher rating than required is used, it may not blow when the current exceeds safe levels, which could lead to overheating, damage to components, or even fire.

70. Explain why household wiring is done in parallel instead of series.

• Answer: Household wiring is done in parallel to ensure that each appliance receives the full voltage and can operate independently. If one appliance fails, others continue to function. In contrast, in a series circuit, all appliances would receive reduced voltage and depend on the functioning of other devices.

Numerical Problems (Continued)

71. If a wire of resistance 5 ohms is stretched to double its length, what will be the new resistance?

• Answer: When the length of the wire is doubled, the resistance also doubles.
  New resistance = 5 ohms * 2 = 10 ohms

72. A 6 V battery is connected to a resistor of 2 ohms. Calculate the power consumed by the resistor.

• Answer: Power (P) = Voltage squared (V²) / Resistance (R)
  P = (6 * 6) / 2 = 36 / 2 = 18 W

73. How much energy is consumed by a 75 W fan running for 4 hours daily over 30 days?

• Answer: Daily energy consumption = 75 W * 4 hours = 300 watt-hours = 0.3 kWh
  Monthly consumption = 0.3 kWh * 30 days = 9 kWh

74. Calculate the current flowing through a 40 W bulb connected to a 200 V supply.

• Answer: Current (I) = Power (P) / Voltage (V)
  I = 40 W / 200 V = 0.2 A

75. A circuit has a total resistance of 15 ohms and a total current of 3 A. What is the total voltage across the circuit?

• Answer: Voltage (V) = Current (I) * Resistance (R)
  V = 3 A * 15 ohms = 45 V

Matching Questions (Continued)

76. Match the type of circuit with its characteristic:
    • (a) Series circuit – (i) Voltage is the same across each component
    • (b) Parallel circuit – (ii) Current is the same through all components
      Answer: (a) – ii, (b) – i
77. Match the physical quantity with its unit:
    • (a) Resistance – (i) Ampere
    • (b) Current – (ii) Ohm
    • (c) Voltage – (iii) Volt
    • (d) Power – (iv) Watt
      Answer: (a) – ii, (b) – i, (c) – iii, (d) – iv
78. Match the component with its function:
    • (a) Fuse – (i) Stores electrical energy
    • (b) Resistor – (ii) Limits current in a circuit
    • (c) Capacitor – (iii) Protects circuit by breaking connection if current is too high
      Answer: (a) – iii, (b) – ii, (c) – i

Long Answer Questions (Continued)

79. Describe the factors affecting the resistance of a conductor and how each factor influences the resistance.

• Answer: The resistance of a conductor is influenced by the following factors:
  • Length: Resistance is directly proportional to the length of the conductor. Doubling the length doubles the resistance.
  • Cross-sectional area: Resistance is inversely proportional to the area. A larger area reduces resistance.
  • Material: Different materials have different resistivities. A material with higher resistivity offers more resistance.
  • Temperature: For most materials, resistance increases with an increase in temperature due to increased atomic vibrations, which impede electron flow.

80. Explain how resistors can be combined in a circuit and the effect of each combination on the total resistance and current.

• Answer: Resistors can be combined in two main ways:
  • Series: In a series circuit, resistors are connected end-to-end. The total resistance is the sum of individual resistances. The current is the same through all resistors, but the voltage drops across each resistor.
  • Parallel: In a parallel circuit, resistors are connected across the same two points. The total resistance is less than the smallest individual resistor, as it provides multiple paths for current. The voltage across each resistor is the same, but the current varies based on resistance.

True/False Questions (Continued)

81. The total voltage in a series circuit is the sum of the voltage drops across each resistor.
    Answer: True
82. The resistivity of a material depends on its length and cross-sectional area.
    Answer: False (Resistivity is a material property and does not depend on the dimensions of the material.)
83. An ammeter has very high resistance.
    Answer: False (An ammeter has very low resistance to ensure it does not affect the current flowing in the circuit.)
84. The resistance of an alloy is usually higher than that of pure metals.
    Answer: True
85. When resistors are connected in parallel, the current through each resistor is the same.
    Answer: False (The current through each resistor in parallel depends on its resistance.)

Numerical Problems (Continued)

86. A circuit has a 9 V battery connected to a resistor of 3 ohms. Calculate the power dissipated by the resistor.

• Answer: Power (P) = Voltage squared (V²) / Resistance (R)
  P = (9 * 9) / 3 = 81 / 3 = 27 W

87. If a wire of resistance 12 ohms is bent to form a circle, what is the resistance between two diametrically opposite points?

• Answer: When bent into a circle, the wire forms two resistances in parallel, each of 6 ohms.
  The equivalent resistance (R) = 1 / (1/6 + 1/6) = 3 ohms

88. Calculate the energy consumed in joules by a 60 W fan running for 5 hours.

• Answer: Energy (E) = Power (P) * Time (T)
  E = 60 W * 5 hours = 300 watt-hours = 300 * 3600 J (since 1 watt-hour = 3600 J)
  E = 1,080,000 J

89. A 240 V electric kettle has a resistance of 48 ohms. Calculate the current flowing through the kettle.

• Answer: Current (I) = Voltage (V) / Resistance (R)
  I = 240 V / 48 ohms = 5 A

90. If four resistors, each of 8 ohms, are connected in parallel, calculate the total resistance.

• Answer: For resistors in parallel:
  1/R_total = 1/8 + 1/8 + 1/8 + 1/8 = 4/8 = 1/2
  R_total = 2 ohms

Matching Questions (Continued)

91. Match the quantity with the correct formula:
    • (a) Power – (i) V = IR
    • (b) Resistance – (ii) P = VI
    • (c) Voltage – (iii) I = Q/t
    • (d) Current – (iv) R = V/I
      Answer: (a) – ii, (b) – iv, (c) – i, (d) – iii
92. Match the application with the appropriate effect of electric current:
    • (a) Electric heater – (i) Heating effect
    • (b) Electric fuse – (ii) Magnetic effect
    • (c) Electric motor – (iii) Heating effect
      Answer: (a) – i, (b) – i, (c) – ii
93. Match the unit with its symbol:
    • (a) Ampere – (i) W
    • (b) Volt – (ii) V
    • (c) Ohm – (iii) A
    • (d) Watt – (iv) Ω
      Answer: (a) – iii, (b) – ii, (c) – iv, (d) – i

Long Answer Questions (Continued)

94. Explain the significance of the power rating of electrical appliances and how it affects their usage.

• Answer: The power rating of an electrical appliance indicates the amount of power it consumes when operated at its rated voltage. It is important for determining the energy consumption of the appliance and helps in selecting the appropriate fuse, wiring, and circuit protection. Appliances with higher power ratings consume more energy, leading to higher electricity bills, and require wiring capable of carrying larger currents.

95. Discuss the precautions one must take while handling electrical circuits and devices.

• Answer: Safety precautions include:
  • Always switching off the power supply before handling any electrical circuit or device.
  • Avoiding contact with live wires or terminals.
  • Using insulated tools and wearing rubber-soled shoes to prevent electric shocks.
  • Ensuring that circuits are not overloaded to prevent overheating and fire hazards.
  • Regularly checking for damaged insulation and replacing faulty wires or components.

96. Describe the role of resistivity in determining the conductivity of a material and its applications in choosing materials for electrical wiring.

• Answer: Resistivity is a measure of how strongly a material opposes the flow of electric current. Materials with low resistivity, like copper and aluminum, are good conductors and are commonly used for electrical wiring. High-resistivity materials are used for resistors, heating elements, and insulating components. The choice of material for a specific application depends on the required balance between conductivity, durability, and cost.

97. Explain how the combination of resistors in series and parallel affects the overall resistance in a circuit. Provide examples of practical applications where each combination is used.

• Answer:
  • In a series combination, the total resistance increases as resistors are added, which reduces the current for a given voltage. This setup is used in applications where a higher resistance is needed, such as in voltage dividers.
  • In a parallel combination, the total resistance decreases, allowing more current to flow through the circuit. This is used in household wiring, where each appliance requires the same voltage but may draw different currents.

98. Why is it important to select the correct fuse rating for electrical appliances, and what could happen if the wrong rating is chosen?

• Answer: Selecting the correct fuse rating is crucial to protect electrical appliances from damage due to excessive current. If a fuse with too high a rating is used, it may not blow in time to prevent overheating, leading to potential fires or damage to the appliance. Conversely, if a fuse with too low a rating is used, it may blow unnecessarily, interrupting the power supply even under normal operating conditions.

99. Discuss the significance of Ohm’s law in understanding and designing electrical circuits. Provide examples of how it is applied in practical scenarios.

• Answer: Ohm’s law is fundamental in understanding the relationship between voltage, current, and resistance in electrical circuits. It is used to design circuits with desired current and voltage characteristics by selecting appropriate resistances. For example, it helps in determining the correct resistor value to use in series with an LED to prevent it from burning out or in calculating the required resistance for a specific power output in heating elements.

100. Explain the importance of grounding in electrical systems and the role it plays in safety.

• Answer: Grounding provides a safe path for excess electric charge to dissipate into the earth, preventing electric shocks and reducing the risk of fire. It ensures that exposed metal parts of electrical devices do not become live, which could otherwise lead to serious injury or death if touched. Grounding is an essential safety feature in household and industrial electrical systems, helping to protect both people and equipment.