A moving coil galvanometer is a device that can measure small electric currents by detecting the magnetic effect of the current on a coil suspended in a magnetic field.
Working Principle
- A rectangular coil of many turns of thin copper wire is wound on a light metallic frame and suspended between the poles of a horseshoe magnet by a thin phosphor-bronze strip.
- A soft iron core is placed inside the coil to enhance the magnetic field and make it radial. A spring is attached to the lower end of the coil to provide a counter torque and a steady deflection.
- A mirror is fixed to the coil to reflect a beam of light on a scale, which helps to measure the angular displacement of the coil.
- When a current is passed through the coil, it experiences a magnetic torque that tends to rotate it. The torque is proportional to the current and the magnetic field strength.
- The coil rotates until the magnetic torque is balanced by the spring torque. The angle of rotation is proportional to the current in the coil.
- The current in the coil can be determined by measuring the deflection of the light beam on the scale.
When a current flows through the coil, a torque acts on it due to the magnetic force on the current-carrying wires. This torque is given by the equation
\(\displaystyle\tau = NIAB\)
where N is the number of turns in the coil, I is the current, A is the area of the coil, and B is the magnetic field. The torque makes the coil rotate until it is balanced by a counter torque provided by a spring attached to the coil. The counter torque is given by
\(\displaystyle\tau’ = k\phi\)
where k is the spring constant and $\phi$ is the angular displacement of the coil. The equilibrium condition is
\(\displaystyle NIAB = k\phi\)
The angular displacement of the coil is proportional to the current in the coil, and it can be measured by a pointer attached to the coil and a scale.
Construction
- Coil: The main component of the galvanometer is a coil of wire, typically made of copper or aluminum. This coil is wound around a lightweight frame, often in the shape of a rectangular or circular loop.
- Frame: The coil is mounted on a lightweight frame that allows it to rotate freely within the galvanometer. The frame is usually made of non-magnetic material to prevent interference with the magnetic field.
- Magnetic Field: Inside the galvanometer, there is a permanent magnet or an electromagnet that creates a strong magnetic field. This magnetic field is essential for the operation of the galvanometer and interacts with the current flowing through the coil.
- Pointer: Attached to the coil is a pointer, typically a small magnetic needle or a thin metal strip. This pointer moves along a scale or dial, indicating the amount of deflection of the coil.
- Scale: A scale or dial is provided next to the pointer to measure the deflection. The scale is marked with units such as milliamperes (mA) or microamperes (μA) to indicate the magnitude of the current being measured.
- Restoring Spring: To ensure that the coil returns to its original position after the current is removed, a restoring spring is attached to it. This spring exerts a force opposite to the direction of rotation, providing a restoring torque.
Sensitivity
The sensitivity of a moving coil galvanometer is defined as the ratio of the angular deflection of the coil to the current in the coil. It is given by
\(\displaystyle S = \frac{\phi}{I}\)
The sensitivity of a moving coil galvanometer depends on the following factors:
- The number of turns in the coil: The sensitivity increases with the number of turns, as the torque on the coil increases.
- The area of the coil: The sensitivity increases with the area of the coil, as the torque on the coil increases.
- The strength of the magnetic field: The sensitivity increases with the strength of the magnetic field, as the torque on the coil increases.
- The spring constant: The sensitivity decreases with the spring constant, as the restoring torque increases.
The sensitivity of a moving coil galvanometer can be increased by using a large number of turns of thin wire, a large area of the coil, a strong magnet, and a soft spring. Sensitivity is of two types, namely, current sensitivity and voltage sensitivity.
Current Sensitivity
The current sensitivity of a moving coil galvanometer is the ratio of the angular deflection of the coil to the current in the coil. It is given by
\(\displaystyle S_i = \frac{\phi}{I}\)
Where,
- \(\displaystyle\phi\) is the angular deflection
- \(\displaystyle S_i\) is the current sensitivity,
- I is the current.
The unit of current sensitivity is degree per ampere or radian per ampere.
Voltage sensitivity
The voltage sensitivity of a moving coil galvanometer is the ratio of the angular deflection of the coil to the voltage across the coil. It is given by
\(\displaystyle S_v = \frac{\phi}{V}\)
where V is the voltage, and \(\displaystyle S_v\) is the voltage sensitivity.
The unit of voltage sensitivity is degree per volt or radian per volt. The voltage sensitivity is related to the current sensitivity and the resistance of the coil by the formula
\(\displaystyle S_v = \frac{S_i}{G}\)
where G is the resistance of the coil. The voltage sensitivity depends on the same factors as the current sensitivity, as well as the resistance of the coil. The voltage sensitivity increases with the resistance of the coil, as the current in the coil decreases.
Conversion to ammeter and voltmeter
A moving coil galvanometer can be converted into an ammeter or a voltmeter by adding suitable resistances in parallel or in series with the coil.
To convert a galvanometer into an ammeter, a low resistance (called a shunt) is connected in parallel with the coil. The shunt allows most of the current to bypass the coil, and only a small fraction of the current passes through the coil. The value of the shunt resistance is calculated by the formula
\(\displaystyle S = \frac{I_g G}{I – I_g}\)
where
- \(\displaystyle I_g\) is current for full-scale deflection of the galvanometer,
- I is the range of the ammeter,
- G is the resistance of the galvanometer.
Let G be the resistance of the galvanometer, \(\displaystyle I_g\) be the current for full-scale deflection of the galvanometer, S be the shunt resistance, and I be the range of the ammeter. The total current I is divided into two parts: \(\displaystyle I_g\) through the galvanometer and \(\displaystyle I – I_g\) through the shunt. The voltage drop across the galvanometer and the shunt is the same, so we have
\(\displaystyle I_g G = (I – I_g) S\)
Rearranging, we get
\(\displaystyle S = \frac{I_g G}{I – I_g}\)
This is the formula for the shunt resistance.
convert a galvanometer into a voltmeter
To convert a galvanometer into a voltmeter, a high resistance is connected in series with the coil. The high resistance limits the current in the coil, and the voltage across the coil is proportional to the voltage to be measured. The value of the series resistance is calculated by the formula
\(\displaystyle R = \frac{V}{I_g} – G\)
where
- V is the range of the voltmeter,
- \(\displaystyle I_g\) is the current for full-scale deflection of the galvanometer,
- G is the resistance of the galvanometer.
Let G be the resistance of the galvanometer, \(\displaystyle I_g\) be the current for full-scale deflection of the galvanometer, R be the series resistance, and V be the range of the voltmeter. The total voltage V is divided into two parts: \(\displaystyle I_g G\) across the galvanometer and \(\displaystyle I_g R\) across the series resistance. The total current \(\displaystyle I_g\) is the same in both the galvanometer and the series resistance, so we have
\(\displaystyle V = I_g G + I_g R\)
Rearranging, we get
\(\displaystyle R = \frac{V}{I_g} – G\)
This is the formula for the series resistance.
Advantages of the moving coil galvanometer
Some of the advantages of the moving coil galvanometer are:
- It has high sensitivity, which means it can detect and measure small currents and voltages with a large deflection of the pointer.
- It is not easily affected by stray magnetic fields, as it is shielded by a soft iron core and a metal case.
- It has a high torque to weight ratio, which means it can produce a large torque with a light coil and a strong magnet.
- It has high accuracy and reliability, as it has a linear scale and a uniform magnetic field.
Drawbacks Of Moving Coil Galvanometer
Some of the drawbacks of the moving coil galvanometer are:
- It can only measure direct current (DC), not alternating current (AC), because the direction of the current affects the deflection of the coil. If AC is applied, the coil will oscillate rapidly and the pointer will not show a steady reading.
- It is affected by errors due to the aging of the instrument, magnets, and spring. Over time, the coil, the spring, and the magnet may lose their properties and affect the accuracy and reliability of the galvanometer. For example, the spring may become loose or stiff, the coil may become corroded or damaged, and the magnet may lose its strength or polarity.
- It has a low resistance, which means it draws a large current from the circuit and affects the potential difference across the circuit. This may alter the behavior of the circuit and introduce errors in the measurement. To overcome this problem, a high resistance is added in series with the galvanometer to convert it into a voltmeter, or a low resistance is added in parallel with the galvanometer to convert it into an ammeter.