How to Use a Metre Bridge to Experimentally Verify Resistance Laws
A meter bridge is considered as an electrical apparatus which is conditioned to govern the resistance of a particular conductor. To calculate the effective series and parallel equivalent of resistances, the meter bridge method is used.
The meter bridge contains a long meter bridge wire length of 1metre, and the meter bridge has two dissimilar segments which are left and right segments. In the left segment, we attach the known resistance, whereas in the right segment that resistance is to be connected, whose charge is to be measured.
A jockey is present which senses the balance point. The length is calculated from the left end which is similarly named zero points to the balance point.
Also, a meter bridge entitled a slide wire bridge is a gadget that operates on the Wheatstone bridge principle. A meter bridge is operated for concluding the unknown resistance of a conductor unlike that in Wheatstone bridge.
How do you Find the Unknown Resistance Using the Meter Bridge?
An apparatus like the meter bridge is employed for measuring the unknown resistance of a coil. The figure given below is the diagram of a beneficial meter bridge tool.
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In this figure,
R is named as the Resistance, P is the resistance approaching from AB, S is the Unknown Resistance, and Q is the resistance between the two joints of B and D.
The long wire is named ‘AC’ 1 m in length, and it is prepared from constantan or manganin possessing a uniform cross-sectional area.
As we know, L1 + L2 = 100 cm
Let’s assume that, L1 = L
We get, L2 = 100 – L
The unknown resistance ‘X’ is obtained from a relation in the given wire can be written as:
\[X = R(\frac{L_{2}}{L_{1}}) = R \frac{(100 - L)}{L}\]
And the material’s specific resistance for a certain wire can be illustrated by this relation; R = (3.14) r2X / l
Where, l = length of the wire, and r = the radius of the cable.
The devices that are necessary for measuring the unknown resistance of a conductor using a meter bridge are:
A resistance box
Galvanometer
Meter bridge
Connecting Wires
Unknown resistance of a length 1 meter
Screw gauge
One way key
Jockey
In the meter bridge, the resistances as of the lateral types are replaced by a wire around 1m of the distance of the uniform cross-section. Another pair consists of one known and an unknown pair of resistances.
The galvanometer’s one part linked next to both resistances. At that time, the other fragment of the wire results in the null point where there is no deflection shown by the galvanometer. In this situation, the bridge is considered balanced.
What is the Combination of Resistance?
Generally, there are two types of circuits, known as parallel and series. Both series and parallel circuits contain above single load.
Resistors can be linked as series, or parallel, or both the series and parallel combination.
In series combinations, two or more resistors can be possible for the connection; only when the same current is travelling through each one of them during some potential difference is supplied transversely to the combination.
The combination’s equivalent resistance available in that series combination can be calculated as the arithmetic summation of all the resistances
As examined, in series circuit electrons can pass through in one path only. At this time, as given in the figure below; the current will be identical traveling through every single resistor. Besides, the voltage will be different across the resistor in the series connection.
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In the parallel circuit, the situation is different here. Electrons can pass through many branches in the particular circuit. Here, the voltage stays normal across each resistor without any voltage rise or drop.
A parallel circuit can be designed in many styles, which indicates that resistors can be organized in various forms. It can be utilized as a current separator.
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To Verify the Law of Combination of Resistance Using Metre Bridge
We have conducted these experiments to calculate & authenticate the laws of combination of resistances using a meter bridge.
To verify the laws of combination series of resistances using a metre bridge
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The resistance available in resistance wire or a coil is given as:
\[r = \frac{(100 - l)}{l} \times R\]
Here,
R = the resistance from the resistance box present at the left gap.
l = the length of the meter bridge wire from zero ends equal to the balance point.
As soon as two resistors r1 and r2 are linked with series connection, the relation for the combined resistance becomes:
Rs = r1 + r2
2. To verify the law of parallel combination of resistance using a metre bridge
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Let’s take two resistances as r1 and r2 are linked with the series connection. The series combination resistance denoted as RS.
Here, Rs = r1 + r2
When they are linked as parallel, the relation for the combined resistance is denoted as Rp
\[R_{p} = \frac{r_{1}r_{2}}{r_{1} + r_{2}}\]
FAQs on Verify Law of Combination of Resistance Using Metre Bridge: Stepwise Guide
1. What is the fundamental principle behind the functioning of a metre bridge?
The metre bridge works on the principle of a balanced Wheatstone bridge. A Wheatstone bridge is balanced when the ratio of resistances in its two arms is equal. In a metre bridge, this condition is met when the jockey is placed at a point (the null point) where the galvanometer shows zero deflection. At this point, the ratio of the unknown resistance (S) to the known resistance (R) is equal to the ratio of the lengths of the bridge wire on either side of the jockey, i.e., S/R = l₂/l₁, where l₁ + l₂ = 100 cm.
2. What is the law of combination for resistances connected in series?
The law of combination for resistances in series states that when two or more resistors are connected end-to-end, their equivalent resistance (Rₛ) is the algebraic sum of their individual resistances. If R₁ and R₂ are two resistances connected in series, the total resistance is given by the formula: Rₛ = R₁ + R₂. The equivalent resistance in a series combination is always greater than the largest individual resistance in the circuit.
3. How is the law of combination for resistances in parallel defined?
The law of combination for resistances in parallel states that when two or more resistors are connected between the same two points, the reciprocal of the equivalent resistance (Rₚ) is the algebraic sum of the reciprocals of their individual resistances. For two resistances, R₁ and R₂, connected in parallel, the formula is: 1/Rₚ = 1/R₁ + 1/R₂. The equivalent resistance in a parallel combination is always smaller than the smallest individual resistance in the circuit.
4. How do you verify the law of series combination of resistances using a metre bridge?
To verify the law of series combination, follow these steps as per the CBSE Class 12 practical syllabus for 2025-26:
Step 1: Use the metre bridge to find the individual resistances of two wires, let's call them r₁ and r₂.
Step 2: Connect these two wires in series and place this combination in the 'unknown resistance' gap of the metre bridge.
Step 3: Find the balancing length (l) and calculate the experimental equivalent resistance (Rₛ) using the metre bridge formula.
Step 4: Calculate the theoretical equivalent resistance by adding the individual resistances: R(theoretical) = r₁ + r₂.
Step 5: Compare the experimental Rₛ with the theoretical value. If they are nearly equal, the law of series combination is verified.
5. Before taking measurements, how can a student confirm that the circuit connections for the metre bridge experiment are correct?
To confirm the connections, touch the jockey gently at the two ends of the metre bridge wire. First, touch the jockey at the 0 cm mark and note the direction of deflection in the galvanometer. Then, touch the jockey at the 100 cm mark. If the circuit is connected correctly, the galvanometer should show a deflection in the opposite direction. If the deflection is in the same direction for both ends, it indicates a fault in the circuit connections that must be rectified.
6. Why is it advised to find the balancing point near the middle (around 50 cm) of the metre bridge wire?
Obtaining the balancing point near the middle of the wire is crucial for maximising the sensitivity of the metre bridge. When the balancing length 'l' is close to 50 cm, the four resistances of the Wheatstone bridge are of a similar order of magnitude. In this condition, a very small displacement of the jockey from the null point results in a large deflection in the galvanometer. This makes the null point sharp and distinct, thereby minimising the percentage error in the measurement of the length and improving the accuracy of the result.
7. What are 'end errors' in a metre bridge experiment, and how can they be minimised?
'End errors' are systematic errors that arise due to several factors, including the resistance of the copper strips at the ends of the bridge wire and non-uniformity in the wire's cross-section near the ends. These cause the zero mark of the scale not to coincide exactly with the start of the 100 cm wire. To minimise this error, you should interchange the positions of the known resistance box (R) and the unknown resistance (S) and take a second set of readings. The average of the two calculated values for the unknown resistance will effectively cancel out the end errors.
8. What happens to the balance point if the positions of the galvanometer and the battery are interchanged in a balanced metre bridge circuit?
If the positions of the galvanometer and the battery (cell) are interchanged in a balanced metre bridge (which is a Wheatstone bridge), the bridge remains balanced. The galvanometer will still show zero deflection at the same null point. This is due to the principle of conjugacy in a Wheatstone bridge, which states that the battery and galvanometer arms are interchangeable when the bridge is in a state of balance without affecting the balance condition.
