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Physics

How to Find Resistance and Resistivity of a Wire Using a Metre Bridge

How to Find Resistance and Resistivity of a Wire Using a Metre Bridge

Stepwise Procedure for Metre Bridge Experiment and Calculating Resistivity

The topic of To Find Resistance Of Given Wire Using Metre Bridge And Hence Determine The Resistivity Of Its Material Experiment is important in physics and helps us understand how to accurately measure electrical resistance and the resistivity of conductors. This experiment is essential for CBSE, JEE, and NEET aspirants, and builds strong fundamentals for electronics and material science.

Understanding the Metre Bridge Experiment to Find Resistance

To find resistance of a given wire using metre bridge and hence determine the resistivity of its material experiment is a classic physics practical. In this method, the resistance of a wire is found using a metre bridge—a practical adaptation of the Wheatstone bridge principle. It helps in understanding related concepts like electrical resistance, specific resistance (resistivity), and electrical measurements, all crucial for advanced studies.

Formula or Working Principle of Resistance Measurement by Metre Bridge

The concept is based on the Wheatstone bridge, where the metre bridge allows you to measure an unknown resistance (X) using a known resistance (R) and the balancing principle where the galvanometer shows no deflection (null point). The relation is:

X = (R × (100 - l)) / l

where R is the known resistance, l is the balancing length (in cm) from one end of the bridge wire. Once X is known, resistivity (specific resistance, ρ) is calculated as:

ρ = (π × r² × X) / L

Here, r is the radius of the wire and L its length. This experiment connects the mathematical and practical concepts of electrical measurements.

Here’s a useful table to understand key concepts better:

Resistance and Resistivity Experiment Table

Concept	Description	Example
Resistance Measurement	Finding unknown resistance by balancing lengths in a metre bridge	Using a wire and standard resistor
Resistivity Calculation	Calculating specific resistance using resistance, length, and radius	Copper wire in physics lab

Worked Example / Practical Experiment

Let’s understand how to perform the experiment step-by-step:

1. Connect the metre bridge as per diagram with a known resistance (R) and the given wire.

2. Place a battery, galvanometer, and jockey as shown in standard physics textbooks.

3. Move the jockey along the wire to find the point where there is no deflection (null point) in the galvanometer. Note the length l (cm) from end A.

4. Use standard formula: X = (R × (100 - l)) / l to calculate the resistance of the wire.

5. Measure the length (L) and diameter/radius (r) of the wire using a scale and screw gauge.

6. Calculate resistivity ρ using the formula: ρ = (π × r² × X) / L.

Conclusion: This method gives accurate values and connects practical circuitry with theoretical formulae in physics.

Practice Questions

Define the aim of finding resistance using metre bridge and explain the key steps.
What is the formula used to calculate unknown resistance in a metre bridge setup?
How does this experiment help in understanding resistivity and material property?
Write the working principle behind the metre bridge method.

Common Mistakes to Avoid

Not tightening the wire or establishing good electrical contact in the circuit.
Incorrectly reading the balancing length (l), leading to calculation errors.
Using a wire of non-uniform thickness—always select a uniform, fresh wire sample.
Confusing SI units—always use meters (m), ohms (Ω), and meters squared (m²) properly.

Real-World Applications

The experiment to find resistance of a wire using metre bridge and hence determine resistivity is widely used in labs, electronics, and quality control of manufacturing wires and cables. The principle is also the basis for more complex measurement devices in the engineering industry. Vedantu helps you build confidence in practical and numerical applications for exams and future learning.

In this article, we explored to find resistance of given wire using metre bridge and hence determine the resistivity of its material experiment—including formulae, practical steps, troubleshooting, and its utility for physics learning. Keep practicing such experiments with Vedantu to deepen your scientific skills and perform better in exams.

FAQs on How to Find Resistance and Resistivity of a Wire Using a Metre Bridge

1. How do I find the resistance of a given wire using a metre bridge?

The metre bridge experiment determines a wire's resistance using the principle of Wheatstone's bridge. You'll connect the unknown wire to one arm of the bridge, a known resistance to another, and a galvanometer to detect the balance point. By measuring the lengths of the bridge wire on either side of the balance point, and knowing the known resistance, you can calculate the unknown wire's resistance using the formula: R_unknown = (L_unknown / L_known) * R_known, where L represents the lengths of the wire segments.

2. How do I determine the resistivity of a wire's material using a metre bridge?

Once you've found the resistance (R) of the wire using the metre bridge, you can calculate its resistivity (ρ). Resistivity is an intrinsic property of the material and is independent of the wire's dimensions. The formula is: ρ = (R * A) / L, where A is the cross-sectional area of the wire and L is its length. You'll need to measure the wire's length and diameter (to calculate A) accurately using a metre scale and screw gauge, respectively.

3. What are the steps involved in performing a metre bridge experiment to find resistance?

The experiment involves these steps: 1. Set up the metre bridge apparatus, connecting the unknown wire and a known resistance. 2. Connect a galvanometer and a battery. 3. Adjust the jockey along the metre bridge wire until the galvanometer shows zero deflection (null point). 4. Measure the lengths of the wire segments (L_unknown and L_known) on either side of the null point. 5. Calculate the unknown resistance using the formula mentioned above. 6. Measure the wire's length and diameter to calculate its resistivity.

4. What is the formula for calculating the resistivity of a wire from metre bridge data?

The resistivity (ρ) of the wire's material is calculated using the formula: ρ = (R * A) / L. Here, R is the resistance of the wire (calculated using the metre bridge), A is the cross-sectional area (πr², where r is the radius), and L is the length of the wire. Ensure consistent units (e.g., ohms for R, square meters for A, and meters for L) for accurate results.

5. How do I write a step-by-step procedure for the metre bridge experiment in my exam?

Your answer should include a clear and concise description of each step. Begin with the setup (connecting the components), then explain how to find the null point, and detail the measurements taken. Include the formulas used for calculating resistance and resistivity. Conclude with a statement of the results and a discussion of any sources of error.

6. What are some common errors to avoid in the metre bridge experiment?

Common errors include: * Loose connections leading to inaccurate readings. * Parallax error while reading the metre scale. * Incorrect placement of the jockey on the wire. * Using a damaged or faulty galvanometer. * Neglecting the end corrections of the metre bridge. Careful attention to setup and precise measurements can minimize these errors.

7. How is the metre bridge experiment related to Wheatstone's bridge?

The metre bridge is a simplified version of the Wheatstone bridge. Wheatstone's bridge is a circuit used to measure unknown resistances by balancing two legs of a bridge circuit. The metre bridge uses a uniform wire as one of the legs, simplifying the setup and making it suitable for practical experiments.

8. What is the significance of the null point in the metre bridge experiment?

The null point, or balance point, is crucial. It's the point on the metre bridge where the galvanometer shows zero deflection. At this point, the ratio of resistances in the two arms of the bridge is equal, allowing for the calculation of the unknown resistance.

9. Why is the metre bridge method preferred for determining resistance?

The metre bridge offers several advantages: * It's relatively simple and inexpensive to set up. * It's easy to use and understand, even for beginners. * It's accurate enough for many applications, especially in educational settings. * It provides a practical application of Wheatstone's bridge principle.

10. How can I improve the accuracy of my metre bridge experiment?

To enhance accuracy: * Use a sensitive galvanometer. * Ensure tight connections. * Avoid parallax error when reading the scale. * Repeat the experiment multiple times and take the average. * Consider end corrections to account for the resistance of the connecting wires at the ends of the bridge wire. * Use a well-calibrated known resistance.

11. What is the difference between resistance and resistivity?

Resistance (R) is a measure of how much a specific component opposes the flow of current, while resistivity (ρ) is a material property that indicates how strongly a material opposes current flow, independent of its shape or size. Resistance depends on both resistivity and the dimensions of the object (R = ρL/A).