Meter bridge
Meter Bridge
The meter bridge, also known as a slide wire bridge, is a simple device used to measure an unknown electrical resistance by balancing two legs of a bridge circuit. It is based on the principle of Wheatstone bridge. The meter bridge is widely used in laboratories to determine the unknown resistance because it is quite accurate and easy to use.
Principle of Operation
The meter bridge operates on the principle of the Wheatstone bridge, which states that when the bridge is balanced, the ratio of the resistances in one arm is equal to the ratio of the resistances in the other arm. Mathematically, this can be expressed as:
$$ \frac{R_1}{R_2} = \frac{R_3}{R_4} $$
where (R_1), (R_2), (R_3), and (R_4) are the resistances in the four arms of the bridge.
Components of a Meter Bridge
A typical meter bridge consists of the following components:
- A one-meter long wire of uniform cross-section and material, known as the bridge wire, stretched over a wooden or metallic base.
- A galvanometer, which is used to detect the null point when the bridge is balanced.
- A jockey, which is a movable contact used to tap the bridge wire at different points.
- Two known resistances (one of which can be variable) and one unknown resistance.
- A battery or a DC power supply to provide a potential difference across the circuit.
Construction and Working
The meter bridge is constructed with a wooden or metallic base with a meter scale marked along its length. A uniform wire, usually made of constantan or manganin, is stretched along the scale. The wire forms one side of the Wheatstone bridge, while the other side is made up of resistances.
The bridge circuit is completed by connecting two known resistances (R_1) and (R_2) in series with the wire, and the unknown resistance (X) and a standard resistance (S) in series with each other. The galvanometer is connected between the junctions of (R_1) and (R_2), and (X) and (S).
To find the unknown resistance (X), the jockey is moved along the wire until the galvanometer shows no deflection, indicating that the bridge is balanced. At this point, the lengths (l_1) and (l_2) of the wire on either side of the jockey are noted. The resistance of the wire is directly proportional to its length, so we can write:
$$ R_1 = \rho \frac{l_1}{A} \quad \text{and} \quad R_2 = \rho \frac{l_2}{A} $$
where (\rho) is the resistivity of the wire and (A) is its cross-sectional area. Since (A) and (\rho) are constant for the wire, the ratio (R_1/R_2) simplifies to (l_1/l_2). Therefore, the unknown resistance (X) can be calculated using the formula:
$$ X = S \frac{l_1}{l_2} $$
Advantages and Disadvantages
| Advantages | Disadvantages |
|---|---|
| Simple and easy to use | Limited to measuring low resistances |
| Inexpensive | Accuracy depends on the uniformity of the bridge wire |
| Provides direct reading of resistance | Parallax errors can occur while reading the scale |
| Does not require external calibration | Contact resistance can affect the results |
Example
Let's consider an example to understand how to use a meter bridge to measure an unknown resistance.
Suppose we have an unknown resistance (X), a standard resistance (S = 10 \Omega), and upon balancing the bridge, the lengths (l_1) and (l_2) are found to be (40 \text{ cm}) and (60 \text{ cm}), respectively.
Using the formula for the unknown resistance:
$$ X = S \frac{l_1}{l_2} = 10 \frac{40}{60} = \frac{400}{60} = 6.67 \Omega $$
Therefore, the unknown resistance (X) is (6.67 \Omega).
Conclusion
The meter bridge is a valuable tool in the field of electrical measurements. It provides a simple and effective method for determining unknown resistances. However, it is important to ensure that the wire is uniform and that proper contact is made with the jockey to avoid errors in measurement. With careful handling and understanding of its limitations, the meter bridge can be a reliable instrument for laboratory experiments and educational purposes.