Tangent galvanometer
Tangent Galvanometer
A tangent galvanometer is an early measuring instrument used for the detection and measurement of electric current. It is based on the magnetic effect of electric current and was widely used before the advent of more accurate and sensitive galvanometers. It operates on the principle that a magnetic field is generated around a current-carrying conductor, and this field can be used to deflect a magnetic needle.
Principle of Operation
The tangent galvanometer consists of a coil of wire through which the current to be measured flows, and a magnetic compass needle placed at the center of the coil. The coil is placed in the horizontal plane, and the compass needle is free to rotate in the same plane. When an electric current passes through the coil, it generates a magnetic field that interacts with the Earth's magnetic field. The compass needle aligns with the resultant of these two fields.
The deflection of the needle from the Earth's magnetic field direction is used to measure the current. The tangent of the angle of deflection (θ) is proportional to the current (I) passing through the coil.
Formula
The mathematical relationship for a tangent galvanometer is given by:
[ I = \frac{B}{2\pi nR} \tan(\theta) ]
Where:
- ( I ) is the current through the coil,
- ( B ) is the magnetic field strength of the Earth,
- ( n ) is the number of turns in the coil,
- ( R ) is the radius of the coil, and
- ( \theta ) is the angle of deflection of the needle.
Construction
A tangent galvanometer typically consists of the following parts:
- A circular coil of wire with a large number of turns.
- A non-magnetic frame to hold the coil in a horizontal plane.
- A compass needle mounted at the center of the coil.
- A scale to measure the angle of deflection of the needle.
Differences and Important Points
| Feature | Tangent Galvanometer | Modern Galvanometer |
|---|---|---|
| Principle | Based on the tangent of the deflection angle | Based on the suspension of a coil in a magnetic field |
| Sensitivity | Less sensitive | More sensitive |
| Usage | Measurement of current | Measurement of current, voltage, and resistance |
| Calibration | Requires knowledge of Earth's magnetic field | Self-contained calibration |
| Accuracy | Less accurate | More accurate |
Examples
Example 1: Calculating Current
Suppose we have a tangent galvanometer with a single loop of wire (n = 1) with a radius of 0.1 m. The Earth's magnetic field strength (B) is (1 \times 10^{-4}) T. If the angle of deflection (θ) is 45 degrees, we can calculate the current (I) as follows:
[ I = \frac{1 \times 10^{-4}}{2\pi \times 1 \times 0.1} \tan(45^\circ) ] [ I = \frac{1 \times 10^{-4}}{0.2\pi} \times 1 ] [ I = \frac{1 \times 10^{-4}}{0.6283} ] [ I \approx 1.59 \times 10^{-4} \, \text{A} ]
Example 2: Effect of Coil Turns
If the number of turns in the coil is increased to 10 (n = 10) and all other factors remain the same, the current can be recalculated as:
[ I = \frac{1 \times 10^{-4}}{2\pi \times 10 \times 0.1} \tan(45^\circ) ] [ I = \frac{1 \times 10^{-4}}{2\pi} \times 1 ] [ I = \frac{1 \times 10^{-4}}{6.283} ] [ I \approx 1.59 \times 10^{-5} \, \text{A} ]
This demonstrates that increasing the number of turns in the coil reduces the current that produces the same deflection angle.
Conclusion
The tangent galvanometer is an important historical instrument that helped scientists and engineers measure electric current in the early days of electrical research. While modern galvanometers have largely replaced it, the tangent galvanometer remains a valuable educational tool for understanding the magnetic effects of electric current and the interaction between magnetic fields.