Question

Find the resistance of a given wire using meter bridge.

Hint:

Do not slide the jockey roughly on the wire as it can damage the wire and make its cross-section non-uniform. Press it gently. Take the readings quickly after closing the key to avoid heating the bridge wire, which would change its resistance.

Answer 1

Step 1: Understanding the Concept:
A meter bridge is a practical application of the Wheatstone bridge, used to measure an unknown resistance. It consists of a one-meter long wire of uniform cross-section stretched on a wooden board. When the bridge is balanced, the ratio of resistances in two arms is equal to the ratio of their corresponding balancing lengths.
Step 2: Key Formula and Apparatus:
Apparatus Required:
A meter bridge, a galvanometer, a resistance box, the given wire whose resistance is to be measured, a primary cell, a jockey, a key, and connecting wires.
Key Formula:
The working principle is the balanced Wheatstone bridge condition. If R is the unknown resistance in the left gap, S is a known resistance from a resistance box in the right gap, and l is the balancing length from the left end (A), then: \[ \frac{R}{S} = \frac{\text{Resistance of wire of length } l}{\text{Resistance of wire of length } (100 - l)} \] Since the wire has uniform resistance per unit length, this simplifies to: \[ \frac{R}{S} = \frac{l}{100 - l} \] Therefore, the unknown resistance is: \[ R = S \left( \frac{l}{100 - l} \right) \] Step 3: Detailed Procedure:
1. Circuit Setup:
- Assemble the circuit as shown in the standard meter bridge diagram.
- Connect the given wire of unknown resistance (R) in the left gap and the resistance box (S) in the right gap of the meter bridge.
- Connect the galvanometer between the central terminal of the bridge and the jockey.
- The primary circuit consists of a cell and a key connected across the ends of the meter bridge wire.
2. Taking Measurements:
- Close the key to allow current to flow.
- Take out a suitable known resistance (e.g., 2 \(\Omega\)) from the resistance box S.
- Gently tap the jockey at one end (A) and then the other end (B) of the wire. The galvanometer should show deflections in opposite directions. This confirms the connections are correct.
- Slide the jockey along the wire to find the null point, where the galvanometer shows zero deflection. This is the balancing length, l.
- Record the value of S and l.
3. Repeating for Accuracy:
- Repeat the experiment for at least four different values of S.
- For each set, calculate the unknown resistance R using the formula.
- It is also good practice to interchange the positions of R and S and repeat the measurements to eliminate any end errors.
Step 4: Calculation and Final Answer:
Calculate the mean of all the values of R obtained.
\[ R_{mean} = \frac{R_1 + R_2 + R_3 + ...}{n} \] The result is stated as: "The resistance of the given wire is \(R_{mean} \pm \Delta R\), where \(\Delta R\) is the mean absolute error."