class 12 notes

Class 12 Physics Notes Chapter 3 () – Lab Manual (English) Book

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Philoid

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Lab Manual (English)
Detailed Notes with MCQs of Experiment number 3 from your Physics Lab Manual. This experiment deals with verifying the laws of combination of resistances, specifically series and parallel combinations, using a metre bridge. This is an important practical application of Ohm's law and the Wheatstone bridge principle, concepts frequently tested in various government exams.

Experiment 3: To verify the laws of combination (series/parallel) of resistances using a metre bridge.

Aim:
To verify the law of combination of resistances in series and parallel using a metre bridge.

Apparatus Required:

  1. Metre Bridge (a slide wire bridge)
  2. Leclanché cell (or Battery Eliminator)
  3. Galvanometer
  4. Resistance Box
  5. Two different resistance wires (or standard resistors), R1 and R2
  6. Jockey
  7. Connecting Wires
  8. Sand Paper (for cleaning wire ends)
  9. Key (one-way key)

Theory:

  1. Metre Bridge Principle:

    • The metre bridge works on the principle of the Wheatstone bridge.
    • A Wheatstone bridge is balanced when the ratio of resistances in adjacent arms is equal, i.e., P/Q = R/S.
    • In a metre bridge setup, it is used to find an unknown resistance (S) by comparing it with a known resistance (R).
    • If the bridge wire (usually 1 meter or 100 cm long, made of Manganin or Constantan) has uniform cross-section and resistivity, the resistance is proportional to length.
    • Let 'l' be the balancing length from one end (say, the end connected to the known resistance R) where the galvanometer shows zero deflection. The resistance of this length is P = σl, where σ is the resistance per unit length.
    • The resistance of the remaining length (100 - l) cm is Q = σ(100 - l).
    • The unknown resistance S is connected in the other gap.
    • At balance condition (null deflection in galvanometer): R / S = P / Q = (σl) / [σ(100 - l)]
    • Therefore, S = R * (100 - l) / l

  2. Law of Resistances in Series:

    • When two resistances R1 and R2 are connected in series, the equivalent resistance (Rs) is the sum of individual resistances.
    • Rs (Theoretical) = R1 + R2
    • We will experimentally determine the value of Rs using the metre bridge and compare it with this theoretical value.

  3. Law of Resistances in Parallel:

    • When two resistances R1 and R2 are connected in parallel, the reciprocal of the equivalent resistance (Rp) is the sum of the reciprocals of individual resistances.
    • 1 / Rp (Theoretical) = 1 / R1 + 1 / R2
    • Or, Rp (Theoretical) = (R1 * R2) / (R1 + R2)
    • We will experimentally determine the value of Rp using the metre bridge and compare it with this theoretical value.

Circuit Diagrams:

  • Diagram 1: Metre bridge setup to find unknown resistance S (where S will be R1, R2, Rs, or Rp in different steps). Known resistance R from the resistance box is in the left gap, unknown S in the right gap. The galvanometer is connected between the midpoint of R and S, and the jockey slides on the bridge wire. The cell is connected across the ends of the bridge wire.
  • Diagram 2: Shows R1 and R2 connected in series. This combination acts as the unknown resistance 'S' in the metre bridge setup (Diagram 1).
  • Diagram 3: Shows R1 and R2 connected in parallel. This combination acts as the unknown resistance 'S' in the metre bridge setup (Diagram 1).

(Note: You must be able to draw these circuit diagrams correctly.)

Procedure:

  1. Setup: Assemble the metre bridge circuit as shown in Diagram 1. Clean the ends of connecting wires and resistance wires using sandpaper. Ensure all connections are tight.
  2. Find R1: Place the first resistance wire (R1) in the right gap (as unknown resistance S). Introduce a suitable known resistance (R) from the resistance box in the left gap. Close the key. Slide the jockey gently along the wire to find the null point (zero deflection in the galvanometer). Record the balancing length 'l' from the end connected to R. Calculate R1 using the formula: R1 = R * (100 - l) / l. Repeat for 2-3 different values of R and find the mean value of R1.
  3. Find R2: Replace R1 with the second resistance wire (R2) in the right gap. Repeat step 2 to find the mean value of R2.
  4. Verify Series Law: Connect R1 and R2 in series (as shown in Diagram 2). Place this series combination in the right gap of the metre bridge. Find its resistance (Rs experimental) using the same procedure as in step 2.
  5. Compare Series Results: Calculate the theoretical value Rs (Theoretical) = R1 + R2 (using the mean values found in steps 2 & 3). Compare Rs (Experimental) with Rs (Theoretical). Calculate the percentage difference if required: [(Experimental - Theoretical) / Theoretical] * 100%.
  6. Verify Parallel Law: Connect R1 and R2 in parallel (as shown in Diagram 3). Place this parallel combination in the right gap of the metre bridge. Find its resistance (Rp experimental) using the same procedure as in step 2.
  7. Compare Parallel Results: Calculate the theoretical value Rp (Theoretical) = (R1 * R2) / (R1 + R2). Compare Rp (Experimental) with Rp (Theoretical). Calculate the percentage difference.

Observations:
(Tables should be drawn to record the following)

  • Table 1: For Resistance R1
    • Serial No. | Resistance from RB, R (Ω) | Balancing length, l (cm) | (100 - l) (cm) | R1 = R(100-l)/l (Ω)
  • Table 2: For Resistance R2
    • Serial No. | Resistance from RB, R (Ω) | Balancing length, l (cm) | (100 - l) (cm) | R2 = R(100-l)/l (Ω)
  • Table 3: For Series Combination (Rs)
    • Serial No. | Resistance from RB, R (Ω) | Balancing length, l (cm) | (100 - l) (cm) | Rs (Exp) = R(100-l)/l (Ω)
  • Table 4: For Parallel Combination (Rp)
    • Serial No. | Resistance from RB, R (Ω) | Balancing length, l (cm) | (100 - l) (cm) | Rp (Exp) = R(100-l)/l (Ω)

Calculations:

  • Mean R1 = ... Ω
  • Mean R2 = ... Ω
  • Mean Rs (Experimental) = ... Ω
  • Rs (Theoretical) = R1 + R2 = ... Ω
  • Percentage Difference (Series) = |(Rs (Exp) - Rs (Theo)) / Rs (Theo)| * 100% = ... %
  • Mean Rp (Experimental) = ... Ω
  • Rp (Theoretical) = (R1 * R2) / (R1 + R2) = ... Ω
  • Percentage Difference (Parallel) = |(Rp (Exp) - Rp (Theo)) / Rp (Theo)| * 100% = ... %

Result:

  1. The experimentally determined value of the series combination (Rs Exp) is found to be approximately equal to the theoretical value (R1 + R2).
  2. The experimentally determined value of the parallel combination (Rp Exp) is found to be approximately equal to the theoretical value [(R1 * R2) / (R1 + R2)].
  3. Within the limits of experimental error, the laws of series and parallel combination of resistances are verified.

Precautions:

  1. Clean the connecting wires and ends of resistance wires thoroughly with sandpaper.
  2. Ensure all connections are tight. Use connecting wires of negligible resistance (thick copper wires).
  3. Do not slide the jockey rigorously on the wire; press it gently. Sliding can wear out the wire, making its cross-section non-uniform.
  4. Avoid keeping the key closed for a long time to prevent heating of the wires (which changes resistance) and draining the cell.
  5. The known resistance (R) taken from the resistance box should be comparable to the unknown resistance (S) to get the balancing point preferably between 30 cm and 70 cm for better accuracy.
  6. Check for zero error or end corrections if necessary, although for verification purposes, consistent measurements are often sufficient. The connections of R and S should be interchanged and the mean balancing length should be used to minimize end errors.

Sources of Error:

  1. The metre bridge wire may not be of uniform area of cross-section.
  2. End resistances: Contact resistance at the terminals where the wire is soldered to the metallic strips might exist.
  3. The resistance of connecting wires might not be negligible.
  4. Heating effect due to current flow can change the resistances.
  5. Error in measuring the balancing length 'l'.
  6. Resistances used (R1, R2, R) might not be exactly equal to their stated values.
  7. Galvanometer sensitivity might affect the precision of the null point.

Viva Voce (Conceptual Questions for Exams):

  1. What is the principle of a metre bridge? (Wheatstone bridge principle)
  2. Why is the bridge called a 'metre bridge'? (Uses a wire of 1-meter length)
  3. Why is the metre bridge wire generally made of alloys like Manganin or Constantan? (High resistivity and low-temperature coefficient of resistance)
  4. Why is it preferred to obtain the balance point near the middle of the wire (around 50 cm)? (Minimizes percentage error in measurement of 'l' and '100-l')
  5. What happens if the known and unknown resistances are interchanged? (The balancing length 'l' will become '100-l')
  6. What is the effect of heating on the resistance of the bridge wire? (Increases resistance, but alloys minimize this effect)
  7. What is 'end error' in a metre bridge and how can it be minimized? (Error due to contact resistance or non-uniformity at ends; minimized by interchanging R and S and taking the mean reading)
  8. Why should the jockey not be slided along the wire? (Can damage the wire, making it non-uniform)
  9. What is the equivalent resistance when 'n' identical resistors 'R' are connected in series? (n*R)
  10. What is the equivalent resistance when 'n' identical resistors 'R' are connected in parallel? (R/n)
  11. If the galvanometer and cell are interchanged in a balanced Wheatstone bridge, will the balance condition be affected? (No, the balance condition remains the same)

Multiple Choice Questions (MCQs):

  1. A metre bridge works on the principle of:
    (a) Ohm's Law
    (b) Kirchhoff's Laws
    (c) Wheatstone Bridge
    (d) Potentiometer

  2. In a metre bridge experiment to find an unknown resistance 'S', a known resistance R = 5 Ω is used. The null point is obtained at l = 40 cm from the end connected to R. The value of S is:
    (a) 5 Ω
    (b) 7.5 Ω
    (c) 3.33 Ω
    (d) 10 Ω

  3. The wire used in a metre bridge is typically made of Manganin or Constantan because these alloys have:
    (a) High resistivity and high-temperature coefficient
    (b) Low resistivity and high-temperature coefficient
    (c) High resistivity and low-temperature coefficient
    (d) Low resistivity and low-temperature coefficient

  4. To verify the law of series combination of resistances R1 and R2 using a metre bridge, the combination (R1 + R2) is treated as:
    (a) The known resistance R
    (b) The unknown resistance S
    (c) The resistance of the bridge wire
    (d) The internal resistance of the cell

  5. For maximum accuracy in a metre bridge experiment, the balance point should ideally be obtained near:
    (a) 10 cm
    (b) 50 cm
    (c) 90 cm
    (d) Either end of the wire

  6. Two resistors R1 = 2 Ω and R2 = 4 Ω are connected in parallel. Their equivalent resistance Rp (Theoretical) is:
    (a) 6 Ω
    (b) 2 Ω
    (c) 1.33 Ω
    (d) 0.75 Ω

  7. If the positions of the known resistance (R) and unknown resistance (S) are interchanged in a metre bridge setup, the new balancing length l' will be related to the original balancing length l as:
    (a) l' = l
    (b) l' = 100 - l
    (c) l' = 100 / l
    (d) l' = l / 100

  8. Which of the following is a significant source of error in the metre bridge experiment?
    (a) Resistance of the galvanometer
    (b) Internal resistance of the cell
    (c) Non-uniformity of the bridge wire
    (d) Capacitance of the connecting wires

  9. When verifying the law of parallel combination, the experimentally measured resistance (Rp Exp) should be compared with:
    (a) R1 + R2
    (b) (R1 * R2) / (R1 + R2)
    (c) R1 - R2
    (d) R1 / R2

  10. Why should the key be inserted only while taking the reading in a metre bridge?
    (a) To save electricity
    (b) To prevent damage to the galvanometer
    (c) To avoid heating of the bridge wire and resistances
    (d) To increase the sensitivity of the bridge

Answers to MCQs:

  1. (c) Wheatstone Bridge
  2. (b) 7.5 Ω [S = R(100-l)/l = 5 * (100-40)/40 = 5 * 60/40 = 5 * 1.5 = 7.5 Ω]
  3. (c) High resistivity and low-temperature coefficient
  4. (b) The unknown resistance S
  5. (b) 50 cm
  6. (c) 1.33 Ω [Rp = (2*4)/(2+4) = 8/6 = 4/3 ≈ 1.33 Ω]
  7. (b) l' = 100 - l
  8. (c) Non-uniformity of the bridge wire
  9. (b) (R1 * R2) / (R1 + R2)
  10. (c) To avoid heating of the bridge wire and resistances

Study these notes carefully, focusing on the principle, procedure, formulas, and precautions. Understanding the 'why' behind each step is crucial for competitive exams. Let me know if any part needs further clarification.

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