Why is only the half deflection method used to find the resistance of a galvanometer?

Principles of the Half-Deflection Method

The Half-Deflection Method is a technique used to measure the internal resistance of a galvanometer. This method is adopted primarily because it is relatively simple and does not require additional precision instruments or complex circuit setups. Below are the reasons for using the half-deflection method along with its underlying principles:

Basic Principles of the Half-Deflection Method

Initial State: First, connect the galvanometer to a known voltage source so that the galvanometer needle reaches full-scale deflection. At this point, the current through the galvanometer is I, assuming the internal resistance of the galvanometer is G.

Adding Resistance: Next, place a variable resistor R in series with the galvanometer branch and adjust this resistor until the galvanometer needle deflects to half its original position. At this moment, the current through the galvanometer has decreased to I/2.

Calculating Galvanometer Resistance: According to Ohm's Law and the voltage divider principle, when the galvanometer's deflection is halved, the voltage across the galvanometer also halves. Therefore, it can be concluded that the voltage across the galvanometer VG equals the voltage across the external resistor VR. Since the current has also been halved, we have:

This means that when the galvanometer's deflection is halved, the value of the external resistor R is equal to the internal resistance G of the galvanometer.

Why Only Use the Half-Deflection Method?

• Simplified Measurement Process: The half-deflection method requires only a simple experimental setup—a power supply, a galvanometer, and a variable resistor. It does not require precise knowledge of the power supply voltage or the exact current values; it only needs to observe changes in the galvanometer needle.

• Avoiding Complex Calculations: Compared to other methods, such as the Wheatstone Bridge method, the half-deflection method does not involve complex balance conditions or equation solving, making it easier to understand and operate.

• Direct Reading: By directly observing the position changes of the galvanometer needle, results can be obtained quickly, reducing measurement time and sources of error.

• Suitable for Educational Demonstrations: For students, this is an intuitive and easy-to-understand method that helps grasp basic circuit concepts and physical laws, such as Ohm's Law and the voltage divider rule.

However, it is important to note that while the half-deflection method is convenient and quick, it also has limitations. For example, if the galvanometer itself exhibits nonlinear response characteristics, this method may not be accurate enough. Additionally, this method relies on visual judgment of the galvanometer needle, which might introduce human error. Therefore, in cases where higher precision is required, more accurate methods such as the aforementioned Wheatstone Bridge method or other high-precision testing equipment are typically used.