Of course! Here is a comprehensive practical write-up for finding the resistance of a given wire using a metre bridge, formatted for a Class 12 CBSE Physics practical file.

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Experiment No: [Your Experiment Number]

Date: [Date of Experiment]

Aim:

To find the resistance of a given wire/standard resistor using a metre bridge.

Apparatus/Material Required:

1. A metre bridge (slide wire bridge).
2. A Leclanche cell or battery eliminator.
3. A galvanometer.
4. A resistance box (0-10 Ω or 0-100 Ω).
5. A jockey.
6. An unknown resistance wire (R).
7. A one-way key.
8. A rheostat.
9. Thick connecting wires.
10. A piece of sandpaper.

Theory:

Wheatstone Bridge Principle:
A metre bridge works on the principle of Wheatstone’s bridge. A Wheatstone bridge consists of four resistances P, Q, R, and S connected in the form of a quadrilateral. When the bridge is balanced (i.e., no current flows through the galvanometer), the ratio of resistances is given by:

P/Q = R/S

Metre Bridge:
A metre bridge consists of a one-meter-long uniform resistance wire (usually made of manganin or constantan) stretched along a wooden or metal scale graduated in centimeters. The wire is mounted between two thick metallic strips with gaps between them.

• The unknown resistance (R) is connected in the left gap.
• A known resistance (S) from the resistance box is connected in the right gap.
• A jockey (sliding contact) is moved along the wire to find the null point (balancing point) where the galvanometer shows zero deflection.

At the balancing point:
If the balancing length (from the left end to the null point) is l cm, then the remaining length is (100 – l) cm.

The resistance of the wire segment of length l is proportional to l, and the resistance of the remaining segment is proportional to (100 – l).

Therefore, at balance:
R/S = l/(100 – l)

Hence, the unknown resistance:
R = S × [l/(100 – l)] Ω

Specific Resistance (Resistivity):
Once R is determined, the specific resistance (ρ) of the material can be calculated using:
ρ = (R × A) / L

Where:

• A = Cross-sectional area of the wire = πr² (r = radius of wire)
• L = Length of the wire

Circuit Diagram:

(Draw a neat, labeled circuit diagram showing the metre bridge setup)

Components to include in the diagram:

• Metre bridge with 1-meter wire AB
• Unknown resistance R in left gap
• Resistance box S in right gap
• Battery/cell connected to points A and B
• Galvanometer connected between junction of R-S and jockey
• Key in the circuit
• Rheostat (optional)
• Jockey touching the wire at point J

Procedure:

1. Setup:

• Clean the ends of all connecting wires with sandpaper to ensure good electrical contact.
• Place the metre bridge on a table and check that the wire is uniform and tightly stretched.

1. Connections:

• Connect the unknown resistance R in the left gap between terminals 1 and 2.
• Connect the resistance box (set to some value, say 5 Ω initially) in the right gap between terminals 3 and 4.
• Connect the battery (with key in series) to the terminals A and B of the metre bridge.
• Connect one terminal of the galvanometer to the junction point between R and S (terminal 2-3).
• Connect the other terminal of the galvanometer to the jockey.

1. Finding the Null Point:

• Close the key to complete the circuit.
• Take out a suitable resistance (say S = 5 Ω) from the resistance box.
• Touch the jockey gently first at the left end (near 0 cm) and then at the right end (near 100 cm) of the wire. Note the direction of deflection of the galvanometer in both cases. The deflections should be in opposite directions.
• Move the jockey gradually along the wire until you find a point where the galvanometer shows zero deflection (null point or balancing point).
• Note the position of the null point on the scale. Let this be l cm from the left end.
• The balancing length should ideally be between 40 cm and 60 cm for accurate results. If not, adjust the value of S in the resistance box.

1. Recording Observations:

• Record the value of S and the balancing length l.
• Repeat the experiment by changing the value of S (e.g., 6 Ω, 7 Ω, 8 Ω, etc.) and finding the corresponding balancing lengths.
• Take at least 4-5 readings.

1. Calculating Unknown Resistance:

• For each observation, calculate the unknown resistance R using the formula:
  R = S × [l/(100 – l)]
• Find the mean value of R.

Observations:

Least count of metre scale = 0.1 cm

Table for finding the unknown resistance R:

Sr. No.	Known Resistance S (Ω)	Balancing Length l (cm)	(100 – l) (cm)	R = S × l/(100-l)
1.	5.0	[e.g., 52.0]	[48.0]	[5.42]
2.	6.0	[e.g., 55.5]	[44.5]	[7.49]
3.	7.0	[e.g., 58.0]	[42.0]	[9.67]
4.	8.0	[e.g., 60.0]	[40.0]	[12.00]
5.	9.0	[e.g., 62.0]	[38.0]	[14.68]

(Note: Fill in your actual experimental values)

Calculations:

Example Calculation (for observation 1):

• S = 5.0 Ω
• l = 52.0 cm
• (100 – l) = 48.0 cm

R = S × [l/(100 – l)]
R = 5.0 × [52.0/48.0]
R = 5.0 × 1.083
R = 5.42 Ω

Mean Value of R:
R_mean = (R₁ + R₂ + R₃ + R₄ + R₅) / 5
R_mean = [Sum of all R values] / 5
R_mean = _ Ω

Optional: To find Resistivity (ρ) of the wire material

Additional Measurements Required:

1. Length of the unknown resistance wire (L) = _ cm = _ m
2. Diameter of the wire using a screw gauge = d = _ cm
3. Radius of the wire, r = d/2 = _ cm = _ m
4. Cross-sectional area, A = πr² = _ m²

Resistivity:
ρ = (R × A) / L
ρ = (_ × ) /
ρ = _ Ω-m

Result:

1. The resistance of the given wire/resistor using the metre bridge is found to be R = _ Ω.
2. (If calculated) The resistivity of the material of the wire is ρ = _ Ω-m.

Precautions:

1. Clean all connections: Use sandpaper to clean the ends of connecting wires and terminals to ensure good electrical contact.
2. Tight connections: All connections should be tight and secure to avoid loose contacts.
3. Key usage: The key should be pressed only when observations are being taken to avoid unnecessary heating of the wire and draining of the battery.
4. Gentle jockey movement: The jockey should be moved gently along the wire without rubbing or scratching it. It should touch the wire vertically and lightly.
5. Balancing length: The balancing length should be between 40 cm and 60 cm for better accuracy. Adjust the resistance S accordingly.
6. Avoid parallax error: The balancing length should be noted carefully by keeping the eye perpendicular to the scale.
7. Uniform wire: Ensure that the metre bridge wire is uniform in thickness and tightly stretched.
8. Zero error: Check for zero error in the metre scale before taking readings.
9. Current direction: Note the deflection of the galvanometer at both ends of the wire to ensure proper connections.
10. No overheating: Do not keep the circuit closed for a long time to prevent heating of the wire, which can change its resistance.
11. Multiple readings: Take several readings with different values of S to minimize experimental errors.
12. Null point detection: The null point should be detected accurately by observing minimum deflection in the galvanometer.

Sources of Error:

1. The metre bridge wire may not be uniform in cross-section.
2. The wire may get heated if current flows for a long time.
3. End resistances at the terminals may affect readings.
4. The resistance box may have some error in its marked values.
5. Parallax error in reading the scale.

Viva Questions:

1. Q: What is the principle of a metre bridge?
   A: Wheatstone bridge principle.
2. Q: Why should the balancing length be near the middle of the wire?
   A: To minimize errors and get accurate results. Extreme positions have higher percentage errors.
3. Q: What is the material of the metre bridge wire?
   A: Manganin or constantan (alloys with high resistance and low temperature coefficient).
4. Q: What happens if the balancing length is less than 20 cm or more than 80 cm?
   A: The percentage error increases. We should change the resistance S to bring the null point near the middle.
5. Q: Why is the key pressed only while taking observations?
   A: To prevent unnecessary heating of the wire and wastage of battery.

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This detailed write-up should help you prepare a complete practical record for your Class 12 Physics examination!