Category: Basic Physics K-Scheme Lab Manual Answer

 Practical No. 05: Determination of equivalent resistance in series connection of resistors.

• The experimental value of the equivalent resistance in series (Rs) was found to be approximately equal to the sum of the individual resistances (R1 + R2).

• It is concluded that for a series combination, the current remains the same through all resistors, but the voltage is shared.
• It is recommended to use resistors whose values are sufficiently different to clearly observe the voltage division.

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• Answer: The rheostat is used to vary the total current in the circuit. This allows us to obtain multiple sets of voltage and current readings for each resistor configuration, which improves the accuracy of the calculated resistance values.

• Answer:
  • Formula: Voltage (V) = Current (I) × Resistance (R)
  • Given Data:
    • Current (I) = 5 A
    • Resistance (R) = 10 Ω

  • Calculation:
    • V = 5 A × 10 Ω
    • V = 50 V

• Answer:
  • Formula for series: R_effective = R1 + R2 + R3
  • Given Data: R1 = 25 Ω, R2 = 50 Ω, R3 = 75 Ω
  • Calculation:
    • R_effective = 25 + 50 + 75
    • R_effective = 150 Ω

• Answer:
  • Explanation: From Ohm’s law, Current (I) = Voltage (V) / Resistance (R). If resistance (R) is constant and voltage is increased to 5V, the new current will also increase five times.

• Answer:
  • Formula: R_equivalent = R1 + R2 + R3
  • Given Data: R1 = 15 Ω, R2 = 10 Ω, R3 = 20 Ω
  • Calculation:
    • R_equivalent = 15 + 10 + 20
    • R_equivalent = 45 Ω

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 Practical No. 04: Determination of specific resistance of given wire.

• The specific resistance calculated from the formula and from the graph are consistent.
• This value is a constant for the material of the wire, as it remained unchanged for different lengths of the wire, confirming the theory.

• It is concluded that the specific resistance is an intrinsic property of the material.
• It is highly recommended to measure the diameter of the wire very precisely using a micrometer, as the area (A) is very sensitive to errors in diameter measurement.

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• Answer: The specific resistance depends only on the material of the wire and its temperature. It is completely independent of the length and cross-sectional area of the wire.

• Answer: Yes, the resistance changes.
  • Reason: Resistance is inversely proportional to the cross-sectional area (A = 3.142 × r²). Therefore, the wire with the larger radius (larger area) will have a lower resistance.

• Answer:
  1. Ammeter-Voltmeter method (using Ohm’s law).
  2. Metre Bridge method (Wheatstone bridge principle).
  3. Using a digital multimeter in resistance mode.
  4. Carey Foster’s bridge method.

• Answer:
  • Given Data:
    • Specific resistance (rho) = 1.678 × 10⁻⁶ Ω-cm
    • Length (L) = 20 m = 2000 cm
    • Diameter (d) = 0.05 cm -> Radius (r) = 0.025 cm

  • Step 1: Calculate Cross-Sectional Area (A)
    • Area (A) = 3.142 × r²
    • Area (A) = 3.142 × (0.025)² = 0.00196375 cm²

  • Step 2: Calculate Resistance (R)
    • Formula: R = (rho × L) / Area
    • R = (1.678 × 10⁻⁶ × 2000) / 0.00196375
    • R = 0.003356 / 0.00196375
    • R = 1.71 Ohms (Ω)

• Answer: No, the specific resistance will not change.
  • Explanation: Specific resistance is an intrinsic property of the material itself, not its shape or size. Doubling the radius changes the wire’s dimensions (increases Area), which changes its total resistance (R), but the material’s specific resistance remains constant.

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• The straight-line graph of Voltage (V) vs. Current (I) passing through the origin confirms that the wire obeys Ohm’s law.
• The resistance value calculated from the slope of the graph matches the average resistance calculated from the observations, validating the experiment.

• Ohm’s law (V = IR) is successfully verified for the given wire.
• It is highly recommended to switch on the circuit only while taking readings to prevent heating of the wire, which can change its resistance.

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• Answer: The rheostat acts as a variable resistor. Its main function is to control and vary the amount of electric current flowing through the circuit, allowing us to take multiple pairs of voltage (V) and current (I) readings.

• Answer:
  • Formula: Resistance (R) = Voltage (V) / Current (I)
  • Given Data:
    • Voltage (V) = 15 V
    • Current (I) = 5 A

  • Calculation:
    • R = 15 V / 5 A
    • R = 3 Ohms (Ω)

• Answer:
  • Variation in Current: From Ohm’s law, Current (I) = Voltage (V) / Resistance (R). If resistance (R) is constant and voltage is increased five times, the current will also increase five times.
  • Dependence on Temperature: Yes, the resistance of a conductor depends on temperature. For most metals, resistance increases with an increase in temperature.

• Answer:
  • Formula: Voltage (V) = Current (I) × Resistance (R)
  • Given Data:
    • Resistance (R) = 25 Ω
    • Current (I) = 250 A

  • Calculation:
    • V = 250 A × 25 Ω
    • V = 6250 V

• Answer: Ohm’s Law states that the electric current (I) flowing through a conductor is directly proportional to the potential difference (V) applied across its ends, provided the physical conditions (like temperature) remain constant.
• Mathematical expression: V = IR (where R is the resistance).

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• It is concluded that consistent and accurate readings can be achieved by using the ratchet to avoid over-tightening.
• It is highly recommended to always determine and apply the zero error correction for every measurement session.

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• Answer: The measuring tool called a micrometer is not typically a direct part of a telescope or microscope. However, the precision screw mechanism, which is the core principle behind the micrometer, is widely used in these instruments for precise focusing.

• Answer: The main types are:
  • Outside Micrometer: For measuring external dimensions.
  • Inside Micrometer: For measuring internal dimensions.
  • Depth Micrometer: For measuring depths of holes and slots.

• Answer: The range of the given micrometer screw gauge is 0 to 2.5 cm.

• Answer:
  • Formula:
    Least Count (L.C.) = Pitch / Number of circular divisions
  • Given Data:
    • Pitch = 1 mm
    • Number of circular divisions (n) = 100

  • Calculation:
    • L.C. = 1 mm / 100
    • L.C. = 0.01 mm

• Answer:
  • Step 1: Find the Pitch
    • Pitch = Distance moved / Number of rotations
    • Pitch = 20 mm / 10 = 2 mm

  • Step 2: Find the Least Count (L.C.)
    • L.C. = Pitch / Number of circular divisions (n)
    • L.C. = 2 mm / 50
    • L.C. = 0.04 mm

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 Practical No. 01: Measurements of dimensions of given object by Vernier caliper.

• The Vernier caliper is a precise instrument for measuring linear dimensions up to 0.002 cm.
• It is highly recommended to always note the zero error and apply its proper correction for every single reading.

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• Answer:
  • The smallest division on the main scale (m) = 0.1 cm
  • The total number of divisions on the Vernier scale (n) = 50

• Answer:
  • Range: The range of the Vernier caliper is 0 to 15 cm.
  • Application 1: Measuring the internal diameter of a pipe, tube, or beaker.
  • Application 2: Measuring the exact depth of a small hole, slot, or recess.

• Answer:
  • Formula:
    Least Count (L.C.) = (Smallest division on main scale) / (Total divisions on Vernier scale)
  • Given Data:
    • Smallest main scale division (m) = 1 mm = 0.1 cm
    • Total Vernier divisions (n) = 20

  • Calculation:
    • L.C. = 0.1 cm / 20
    • L.C. = 0.005 cm (or 0.05 mm)

• Answer:
  • Given Data:
    • Main Scale Reading (MSR) = 7.3 cm
    • Vernier Scale Division (VSD) = 5
    • Least Count (L.C.) = 0.01 cm

  • Step-by-Step Calculation:
    1. Vernier Scale Reading (VSR):
       • VSR = VSD × L.C.
       • VSR = 5 × 0.01 cm = 0.05 cm

    2. Total Reading (Correct Measurement):
       • Total Reading = MSR + VSR
       • Total Reading = 7.3 cm + 0.05 cm = 7.35 cm

  • Conclusion: The correct length of the pencil is 7.35 cm.

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