Of course! Here is a comprehensive practical write-up for verifying the laws of series combination of resistances 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 verify the laws of combination of resistances in series using a metre bridge.

Apparatus/Material Required:

1. A metre bridge (slide wire bridge).
2. A Leclanche cell or battery eliminator (2V).
3. A galvanometer.
4. A resistance box (0-10 Ω).
5. Two resistance wires/resistors of known values (R₁ and R₂).
6. A jockey.
7. A one-way key.
8. A rheostat (optional).
9. Thick connecting wires.
10. A piece of sandpaper.

Theory:

Wheatstone Bridge Principle:
A metre bridge works on the principle of Wheatstone’s bridge. When the bridge is balanced (galvanometer shows zero deflection), the ratio of resistances is:

P/Q = R/S

For a metre bridge, if the balancing length is l cm from the left end, then:

R/S = l/(100 – l)

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

Series Combination of Resistances:
When two or more resistances are connected end to end (in series), the same current flows through each resistance. The total or equivalent resistance is equal to the sum of the individual resistances.

For two resistances R₁ and R₂ connected in series:

R_s = R₁ + R₂

Verification:
In this experiment, we will:

1. Find the individual resistances R₁ and R₂ separately using the metre bridge.
2. Connect R₁ and R₂ in series and find the combined resistance R_s using the metre bridge.
3. Verify that R_s = R₁ + R₂ (within experimental limits).

Circuit Diagram:

(Draw three separate circuit diagrams)

Diagram 1: To find R₁

• Show R₁ in the left gap
• Resistance box S in the right gap
• Complete metre bridge circuit

Diagram 2: To find R₂

• Show R₂ in the left gap
• Resistance box S in the right gap
• Complete metre bridge circuit

Diagram 3: To find R_s (R₁ and R₂ in series)

• Show R₁ and R₂ connected in series in the left gap
• Resistance box S in the right gap
• Complete metre bridge circuit

Components to include:

• Metre bridge with wire AB (100 cm)
• Battery/cell with key
• Galvanometer with jockey
• Resistance box
• Unknown resistances

Procedure:

Part A: To find the resistance R₁

1. Clean the ends of all connecting wires with sandpaper.
2. Connect the first resistance R₁ in the left gap of the metre bridge (between terminals 1 and 2).
3. Connect the resistance box in the right gap (between terminals 3 and 4).
4. Complete the circuit by connecting the battery, key, galvanometer, and jockey as shown in the circuit diagram.
5. Take out a suitable resistance (say S = 2 Ω) from the resistance box.
6. Insert the key and touch the jockey at both ends of the wire to check that the galvanometer shows opposite deflections.
7. Move the jockey along the wire to locate the null point (balancing point) where the galvanometer shows zero deflection.
8. Ensure the balancing length (l₁) is between 40 cm and 60 cm. If not, adjust the value of S.
9. Note the balancing length l₁.
10. Change the value of S and repeat the observations at least 3-4 times.
11. Calculate R₁ for each observation using: R₁ = S × [l₁/(100 – l₁)]
12. Find the mean value of R₁.

Part B: To find the resistance R₂

13. Remove R₁ from the left gap and replace it with R₂.
14. Repeat steps 5 to 12 to find the balancing lengths and calculate R₂.
15. Find the mean value of R₂.

Part C: To find the series combination resistance R_s

16. Remove R₂ from the left gap.
17. Connect R₁ and R₂ in series in the left gap. Connect one end of R₁ to terminal 1 and the other end of R₁ to one end of R₂. Connect the free end of R₂ to terminal 2.
18. Repeat steps 5 to 12 to find the balancing lengths and calculate R_s.
19. Find the mean value of R_s.

Part D: Verification

20. Calculate the sum (R₁ + R₂) and compare it with R_s.
21. Verify that R_s ≈ (R₁ + R₂) within experimental limits.

Observations:

Least count of metre scale = 0.1 cm

Table 1: To find resistance R₁

Sr. No.	Resistance from Box S (Ω)	Balancing Length l₁ (cm)	(100 – l₁) (cm)	R₁ = S × l₁/(100-l₁)
1.	2.0	[e.g., 48.5]	[51.5]	[1.88]
2.	3.0	[e.g., 56.0]	[44.0]	[3.82]
3.	4.0	[e.g., 60.5]	[39.5]	[6.13]
4.	5.0	[e.g., 63.8]	[36.2]	[8.81]

Mean value of R₁ = _ Ω (e.g., 5.16 Ω)

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Table 2: To find resistance R₂

Sr. No.	Resistance from Box S (Ω)	Balancing Length l₂ (cm)	(100 – l₂) (cm)	R₂ = S × l₂/(100-l₂)
1.	3.0	[e.g., 52.0]	[48.0]	[3.25]
2.	4.0	[e.g., 57.5]	[42.5]	[5.41]
3.	5.0	[e.g., 60.8]	[39.2]	[7.76]
4.	6.0	[e.g., 63.0]	[37.0]	[10.22]

Mean value of R₂ = _ Ω (e.g., 6.66 Ω)

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Table 3: To find series combination resistance R_s

Sr. No.	Resistance from Box S (Ω)	Balancing Length l_s (cm)	(100 – l_s) (cm)	R_s = S × l_s/(100-l_s)
1.	6.0	[e.g., 50.5]	[49.5]	[6.12]
2.	8.0	[e.g., 56.8]	[43.2]	[10.52]
3.	10.0	[e.g., 60.0]	[40.0]	[15.00]
4.	12.0	[e.g., 62.5]	[37.5]	[20.00]

Mean value of R_s = _ Ω (e.g., 12.91 Ω)

Calculations:

Example Calculation (for R₁, observation 1):

• S = 2.0 Ω
• l₁ = 48.5 cm
• (100 – l₁) = 51.5 cm

R₁ = S × [l₁/(100 – l₁)]
R₁ = 2.0 × [48.5/51.5]
R₁ = 2.0 × 0.942
R₁ = 1.88 Ω

Mean Values:

• Mean R₁ = (Sum of all R₁ values) / 4 = _ Ω (e.g., 5.16 Ω)
• Mean R₂ = (Sum of all R₂ values) / 4 = _ Ω (e.g., 6.66 Ω)
• Mean R_s = (Sum of all R_s values) / 4 = _ Ω (e.g., 12.91 Ω)

Theoretical value of series combination:
R₁ + R₂ = 5.16 + 6.66 = 11.82 Ω

Experimental value:
R_s = 12.91 Ω

Percentage Error:
Percentage Error = |[(R₁ + R₂) – R_s] / (R₁ + R₂)| × 100
Percentage Error = |(11.82 – 12.91) / 11.82| × 100
Percentage Error = 9.2%

Result:

1. The individual resistances are found to be:

• R₁ = _ Ω
• R₂ = _ Ω

1. The equivalent resistance of R₁ and R₂ in series is:

• R_s = _ Ω (experimental)
• R₁ + R₂ = _ Ω (theoretical)

1. Within experimental limits, R_s ≈ R₁ + R₂, thus verifying the law of series combination of resistances.

Precautions:

1. Clean connections: All wire ends, terminals, and connecting points should be cleaned with sandpaper to ensure good electrical contact.
2. Tight connections: All connections should be tight and secure to avoid loose contacts which can cause errors.
3. Key pressed only during observations: The key should be pressed only when taking readings to prevent heating of the wire and unnecessary battery drain.
4. Gentle jockey movement: The jockey should touch the wire gently and perpendicularly without rubbing or scratching it.
5. Balancing length range: The balancing length should be between 40 cm and 60 cm for accurate results. Adjust resistance S if needed.
6. Avoid parallax error: Note the balancing length by keeping the eye perpendicular to the scale.
7. Check deflection direction: Before finding the null point, check that the galvanometer shows opposite deflections at the two ends of the wire.
8. Uniform wire: Ensure the metre bridge wire is uniform in thickness and tightly stretched.
9. Zero error check: Check for zero error in the metre scale before starting.
10. Multiple readings: Take at least 3-4 readings with different values of S to minimize random errors.
11. Proper series connection: When connecting R₁ and R₂ in series, ensure they are connected end to end with no parallel branches.
12. Avoid overheating: Do not keep the circuit closed for extended periods to prevent heating effects.

Sources of Error:

1. The metre bridge wire may not be perfectly uniform in cross-section.
2. Resistance of the wire may change due to heating when current flows for a long time.
3. End resistances at the terminals and thick strips may introduce errors.
4. The resistance box may have calibration errors.
5. Parallax error while reading the balancing length.
6. Loose connections can introduce contact resistance.
7. External electromagnetic interference may affect the galvanometer.

Viva Questions:

1. Q: State the law of series combination of resistances.
   A: When resistances are connected in series, the equivalent resistance is equal to the sum of individual resistances: R_s = R₁ + R₂ + R₃ + …
2. Q: What is the current through each resistance in series combination?
   A: The same current flows through all resistances connected in series.
3. Q: What is the principle of a metre bridge?
   A: Wheatstone bridge principle, based on balancing of resistances.
4. Q: Why should the balancing length be near 50 cm?
   A: To minimize percentage error in measurements. Extreme positions have higher errors.
5. Q: What is the advantage of using a metre bridge over a Wheatstone bridge?
   A: In a metre bridge, the ratio P/Q can be varied continuously by moving the jockey, making it more versatile.
6. Q: Why is manganin or constantan used for the metre bridge wire?
   A: These alloys have high specific resistance and low temperature coefficient of resistance, ensuring stable measurements.
7. Q: What happens to the total resistance when more resistances are added in series?
   A: The total resistance increases.
8. Q: What would happen if R₁ and R₂ were connected in parallel instead?
   A: The equivalent resistance would be less than the smallest individual resistance: 1/R_p = 1/R₁ + 1/R₂
9. Q: Why do we use a galvanometer instead of an ammeter?
   A: A galvanometer is more sensitive and can detect very small currents, which is necessary for finding the null point accurately.
10. Q: What is the formula for percentage error?
    A: Percentage error = |(Experimental value – Theoretical value) / Theoretical value| × 100

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This detailed write-up provides everything needed for a complete practical record for your Class 12 Physics examination!