Minimizing Percentage Error in Measuring Resistance with a Meter Bridge

When measuring resistance with a meter bridge, it is important to minimize the percentage error to obtain accurate results. The balancing point is a crucial factor that affects the percentage error, and adjusting it close to a particular point can help minimize the error.

What is a Meter Bridge?

A meter bridge is a device used to measure the resistance of a conductor by comparing it with a known resistance. It consists of a wire of uniform cross-sectional area, with a resistance R, stretched over a wooden board. A jockey is used to make contact with the wire at different points. When a battery is connected to the wire, a potential difference is created, and a galvanometer can be used to measure the current flowing through the wire.

What is the Balancing Point?

The balancing point is the point on the wire where the unknown resistance is equal to the known resistance. The jockey is moved along the wire until the galvanometer reads zero, indicating that the potential difference across the wire is zero. At this point, the ratio of the lengths of the wire on either side of the jockey is equal to the ratio of the unknown resistance to the known resistance.

How does Adjusting the Balancing Point Minimize Percentage Error?

The percentage error in measuring resistance with a meter bridge can be calculated using the formula:

Percentage error = (Error/Reading) x 100%

where Error is the difference between the true value and the measured value, and Reading is the measured value.

Adjusting the balancing point close to certain points can minimize the percentage error as follows:

- 0 cm: Adjusting the balancing point close to 0 cm can minimize the error because any slight movement in the jockey will cause a large change in the galvanometer reading, making it easier to detect and correct any errors. However, this method is not recommended for low-resistance measurements because the resistance of the connecting wires and jockey may affect the readings.

- 20 cm: Adjusting the balancing point close to 20 cm can minimize the error because this is the midpoint of the wire, and any slight errors in measurement will be balanced out. This method is recommended for measuring resistances between 1 Ω to 10 Ω.

- 50 cm: Adjusting the balancing point close to 50 cm can minimize the error because this is the point where the wire has the least resistance, and any errors in measurement will have the least effect. This method is recommended for measuring high-resistance values above 100 Ω.

- 100 cm: Adjusting the balancing point close to 100 cm can minimize the error for low-resistance measurements because the resistance of the connecting wires and jockey will have the least effect. However, this method is not recommended for high-resistance measurements because any slight errors in measurement will be magnified.

Conclusion

In conclusion, adjusting the balancing point close to certain points can minimize the percentage error in measuring resistance with a meter bridge. The choice of balancing point depends on the range of resistance being measured and the accuracy required. It is important to take into account the resistance of the connecting wires and jockey and to ensure that they are kept constant throughout the measurement.

The answer is 50
to minimize the percentage error the balancing point is adjusted at the mid point of the meter bridge