Moving coil galvanometer
Moving Coil Galvanometer
A moving coil galvanometer is an instrument used for detecting and measuring small electric currents. It operates on the principle that a current-carrying coil placed in a magnetic field experiences a torque.
Principle of Operation
The moving coil galvanometer works on the principle of the motor effect. According to this principle, when a current-carrying conductor is placed in a magnetic field, it experiences a force. If the conductor is free to move, it will rotate until the force is balanced by the restoring torque of a spring or some other mechanism.
Construction
A typical moving coil galvanometer consists of the following parts:
- Magnetic Core: A strong permanent magnet with a cylindrical soft iron core to produce a radial magnetic field.
- Coil: A rectangular coil of many turns of fine insulated copper wire wound on a light aluminum frame.
- Suspension: The coil is suspended by a phosphor bronze strip, which also serves as a conductor of electricity to and from the coil.
- Pivot: A spring or hair suspension system that provides a restoring torque and also conducts current.
- Pointer: Attached to the coil, it moves over a calibrated scale to indicate the magnitude of the current.
- Damping: A mechanism to prevent oscillations of the coil, often using air damping or eddy current damping.
Working
When a current passes through the coil, it experiences a magnetic torque due to the magnetic field of the permanent magnet. The coil rotates, and the pointer attached to it moves over the scale. The deflection of the pointer is proportional to the current passing through the coil.
Formula
The torque ($\tau$) experienced by the coil is given by:
$$ \tau = nIBA\sin\theta $$
where:
- $n$ is the number of turns in the coil
- $I$ is the current through the coil
- $B$ is the magnetic field strength
- $A$ is the area of the coil
- $\theta$ is the angle between the normal to the coil and the magnetic field (for a radial field, $\theta = 90^\circ$ and $\sin\theta = 1$)
The restoring torque provided by the suspension is:
$$ \tau_{restoring} = -k\phi $$
where:
- $k$ is the torsional constant of the suspension
- $\phi$ is the angle of twist
At equilibrium, $\tau = \tau_{restoring}$, so:
$$ nIBA = k\phi $$
The current can be found by:
$$ I = \frac{k\phi}{nBA} $$
Sensitivity
The sensitivity of a galvanometer is defined as the deflection per unit current. It can be increased by:
- Increasing the number of turns $n$.
- Using a stronger magnetic field $B$.
- Increasing the area of the coil $A$.
- Decreasing the torsional constant $k$.
Differences and Important Points
| Feature | Moving Coil Galvanometer | Other Galvanometers (e.g., Moving Iron) |
|---|---|---|
| Principle | Based on the motor effect | Based on the magnetic effect of current |
| Current Type | Measures direct current (DC) | Can measure alternating current (AC) as well |
| Sensitivity | High sensitivity | Generally less sensitive |
| Damping | Air or eddy current damping | May use different damping methods |
| Direction of Deflection | Deflection direction depends on current direction | Deflection is independent of current direction |
| Construction | Requires a radial magnetic field | Does not require a radial magnetic field |
| Usage | Used for precise measurements | Used for rough measurements or where AC is involved |
Examples
Example 1: Calculating Sensitivity
Suppose a moving coil galvanometer has 50 turns, each with an area of $2 \times 10^{-4} \text{ m}^2$, and is placed in a magnetic field of $0.2 \text{ T}$. The torsional constant of the suspension is $10^{-9} \text{ Nm/degree}$. Calculate the sensitivity of the galvanometer.
Solution: The sensitivity $S$ is given by:
$$ S = \frac{\text{Deflection (degrees)}}{\text{Current (A)}} $$
Using the equilibrium condition:
$$ I = \frac{k\phi}{nBA} $$
The sensitivity is:
$$ S = \frac{\phi}{I} = \frac{nBA}{k} $$
Substituting the values:
$$ S = \frac{50 \times 0.2 \times 2 \times 10^{-4}}{10^{-9}} $$ $$ S = 2 \times 10^{3} \text{ degrees/A} $$
Example 2: Effect of Reversing Current
If the current through the moving coil galvanometer is reversed, what happens to the deflection?
Solution: Since the deflection direction depends on the current direction, reversing the current will cause the pointer to deflect in the opposite direction. The magnitude of deflection will remain the same for the same magnitude of current.
In conclusion, the moving coil galvanometer is a sensitive and precise instrument for measuring small DC currents. Its design and operation principles allow for accurate readings, which are essential in various scientific and industrial applications.