Verification of Laws of Combination of Resistances:

Objective:

To verify the series combination law:Rs=R1+R2  and also

to verify the parallel combination law: Rp=R1R2/R1+R2  using a meter bridge.

Theoretical Values:

Series combination of resistors: Rs=2+3  = 5 Ω

Parallel combination of resistors:Rp=2×3/2+3   =6/5  = 1.2 Ω

Apparatus Required:

Meter bridge (wire length=100 cm)

Resistance box (Dial type or plug type) of Known resistance value (R)

Unknown resistance coils (say 2 Ω and 3 Ω)

Galvanometer 30-0-30 range

Leclanché cell (for steady emf)

One way plug key

Pencil Jockey

Connecting wires (D.C.C. Copper)

Principle:

The meter bridge operates on the Wheatstone bridge principle. At balance condition

Resistance in the left gap(AB)/Resistance in the right gap(BC) = l/100-l

Where l = balancing length from left end.

Procedure:

Series Combination: R1+R2= 5 Ω

Place the resistance box (R) in the left gap

Connect R1  and R2  in series in the right gap of the meter bridge.

Change the known resistance value and find the balancing length (where the galvanometer shows null deflection).

Calculate R_s using

R/Rs  =l/100-l

Rs = R  (100-l)/l

For Parallel Combination:

( R1|| R2=1.2 Ω)

Place the resistance box (R) in the left gap

Connect R1  and R2 in parallel in the right gap

Repeat the balancing process for different R values

Calculate Rp using

Rp = R (100-l)/l

Verify if  Rp ≈ 1.2 Ω

Observations for to calculate R1:

S. No	Known Resistance (R)	Balancing length AJ=AD=l	Balancing Length JC=DC=(100-l)	Unknown resistance R1= R (100-l)/l
	(in ohms)	(in cm)	(in cm)	(in ohms)
1.	1.5	42	58	2.07
2.	1.4	41	59	2.01
3.	1.2	37	63	2.04
			Mean R1	2.06

Observations for to calculate R2 :

S. No	Known Resistance (R)	Balancing length AJ=AD=l	Balancing Length JC=DC=(100-l)	Unknown resistance R2= R (100-l)/l
	(in ohms)	(in cm)	(in cm)	(in ohms)
1.	2.5	46.2	53.8	2.91
2.	2.6	47.2	52.8	2.91
3.	2.7	47.8	52.2	2.95
4.	2.9	49.9	50.1	2.91
			Mean R2	2.92

Observations & Calculations for Series Combination:

S. No	Known Resistance (R)	Balancing length AJ=AD=l	Balancing Length JC=DC=(100-l)	Unknown resistance Rs= R(100-l)/l
	(In ohms)	(in cm)	(in cm)	(in ohms)
1.	4	44.4	55.6	5.01
2.	5	50.0	50.0	5.00
3.	6	54.5	45.5	5.01
4.	7	58.3	41.7	5.01
			Mean	5.01

Observations & Calculations for Parallel Combination:

S. No	Known Resistance (R)	Balancing length AJ=AD=l	Balancing Length JC=DC=(100-l)	Unknown resistance = R
	(In ohms)	(in cm)	(in cm)	(in ohms)
1.	1.0	45.5	54.5	1.20
2.	1.2	50.0	50.0	1.20
3.	1,5	55.6	44.4	1.20
4.	2.0	62.5	37.5	1.20
			Mean	1.20

Result for Series combination of resistors:

Theoretical value Rs = 4.98 Ω

Experimental value Rs  = 5 Ω (small error in measurement)

Law verified

Result for parallel combination of resistors:

Theoretical value  Rp = 1.21 Ω

Experimental value Rp = 1.20 Ω (small error in measurement)

Law verified.

Viva-voce Questions

1. What is a meter bridge?
2. What is the principle of a meter bridge?
3. How do you find the unknown resistance using a meter bridge?
4. What is meant by the balancing length in the meter bridge?
5. State the law of combination of resistances in series?
6. State the law of combination of resistances in parallel
7. What is the role of the galvanometer in the meter bridge experiment?
8. Why is jockey used in the meter bridge experiment?
9. Why are alloys like manganin or constantan preferred for the bridge wire?
10. What precautions should be taken during the experiment?
11. What is the function of the resistance box in this experiment?
12. How do you verify the laws of series combination using a meter bridge?
13. How do you verify the laws of parallel combination using a meter bridge?
14. What is the effect of non-uniform wire thickness in the meter bridge?
15. Why is the balance point ideally between 40 cm and 60 cm?
16. What could cause errors in this experiment?
17. Why should the key be inserted only while taking readings?
18. What is the use of Leclanché cell or battery eliminator in the setup?
19. Hat is the formula for equivalent resistance of two resistors in parallel?
20. Why is the Wheatstone bridge considered a null method?

Answers:

1. An electrical device used to measure the unknown resistance based on the Wheatstone bridge principle. It consists of a one-meter-long uniform wire stretched over a scale.
2. Wheatstone bridge principle, which states that at balance condition, the ratio of resistances in one arm equals the ratio of other arm, resulting in no current through the galvanometer.
3. By adjusting the jockey to find the balancing length for null deflection. For the formula refer the experiment.
4. It is the length from one end of the wire to the point where the galvanometer shows zero deflection, indicating balanced Wheatstone bridge.
5. Total resistance is the sum of the individual resistances. Refer the formula given in the experiment.
6. The reciprocal of the total resistance is equals the sum of reciprocals of the individual resistances. For the formula, refer the experiment.
7. Galvanometer detects the presence of current and helps find the balance point indicating zero deflection at equilibrium.
8. Used to make contact along the wire to find the balancing point accurately.
9. Alloys have low temperature coefficients of resistance, ensuring the wire’s resistance remains stable during the experiment.
10. Ensure connections are tight and clean. |Clean wire ends with sandpaper. | Move the jockey gently |Insert the key only while taking readings to avoid heating.

11. It provides known resistance for comparison with unknown resistances to achieve balance in the bridge.
12. Measure the resistance of each coil separately, then connect them in series and measure the combined resistances. The sum should match the combined measurement within experimental error.
13. Measure each resistance separately, then connect them in parallel and measure the combined resistance. The reciprocal of the combined resistance should equal the sum of the reciprocals of individual resistances.
14. Non-uniform thickness causes inaccurate resistance measurements, as resistance is proportional to length if the cross-section is uniform.
15. This ensures greater accuracy, as extreme ends may have contact resistance or non-uniformity affecting readings.
16. Loose connections | non-uniform wire | parallax error in reading lengths | Heating of ire due to prolonged currents.
17. To prevent unnecessary heating of the wire, which can change its resistance and affect accuracy
18. It provides steady source of emf for the circuit.
19. Rp=R1R2/R1+R2
20. Because measurements are made at the point of zero current through the galvanometer, minimizing the effect of instrument resistance for greater accuracy.

 

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