Galvanometer – A Device to Detect Electric Current

Imagine you're in a physics lab, experimenting with measuring the current flowing through a circuit. To accurately measure the current, you need a device that can detect and quantify it. The device that allows you to do that is called a galvanometer.

Table of Contents:

What is a Galvanometer?
What is a Moving Coil Galvanometer?
Construction and Diagram of Moving Coil Galvanometer
Sensitivity of Moving Coil Galvanometer
Conversion of Galvanometer to Ammeter
Conversion of Galvanometer to Voltmeter

What is a Galvanometer?

A galvanometer is a device that is used to detect a small electric current or measure its magnitude. The current and its intensity are usually indicated by a magnetic needle’s movement or that of a coil in a magnetic field, which is an important part of a galvanometer.

What is a Moving Coil Galvanometer?

A moving coil galvanometer is a type of galvanometer that consists of a rectangular coil of wire placed in a uniform radial magnetic field. The coil is free to rotate about a fixed axis and is connected to a circuit that carries the current to be measured. A spring or a strip is attached to the coil to provide a restoring torque and an electrical contact. A pointer or a mirror is attached to the coil to indicate the deflection or rotation of the coil.

The moving coil galvanometer works on the principle that the deflection or rotation angle is proportional to the current in the coil. This can be expressed by the formula:

where ‘I’ is the current in the coil, ‘k’ is the spring or strip constant, ‘θ’ is the deflection or rotation angle, ‘n’ is the number of turns in the coil, ‘B’ is the magnetic field strength, and ‘A’ is the area of the coil.

The moving coil galvanometer can be used to measure small currents, as it has a high sensitivity and a low resistance. It can also be converted into an ammeter or voltmeter using suitable shunts or multipliers.

Construction and Diagram of Moving Coil Galvanometer

The diagram of the moving coil galvanometer is shown below:

galvanometer

The construction of this galvanometer is as follows:

The moving coil galvanometer consists of a rectangular wire coil with many turns and is usually made of thinly insulated or fine copper wire. The coil is wound on a metallic frame and is free to rotate about a fixed axis.
The coil is suspended in a uniform radial magnetic field that is produced by a permanent magnet or an electromagnet. A cylindrical soft iron core is symmetrically positioned inside the coil to improve the strength of the magnetic field and to make the field radial.
The lower part of the coil is attached to a phosphor-bronze spring that has a small number of turns. The other end of the spring is connected to a binding screw. The spring serves two purposes: it provides a restoring torque that balances the magnetic torque and hence produces a steady angular deflection, and it provides an electrical contact for the current to enter or leave the coil.
The upper part of the coil is attached to a phosphor-bronze strip that is connected to a movable torsion head. The strip also serves two purposes: it provides another electrical contact for the current to enter or leave the coil, and it allows the adjustment of the initial position of the coil by rotating the torsion head.
A plane mirror and a lamp, and a scale arrangement are attached to the suspension wire. The mirror reflects a beam of light onto a distant scale, which helps in measuring the deflection of the coil with high accuracy and without parallax error.
A pointer may also be attached to the coil, which indicates the deflection on a nearby scale.

Working Principle of the Moving Coil Galvanometer

The working principle of a moving coil galvanometer can be explained as follows:

When a current flows through the coil, it experiences a magnetic force due to the magnetic field. The force acts perpendicular to both the direction of the current and the direction of the magnetic field.
The force causes a torque on the coil, which makes it rotate about its axis. The torque is given by:

where ‘τ’ is the torque, n is the number of turns in the coil, ‘I’ is the current in the coil, ‘A’ is the area of the coil, ‘B’ is the magnetic field strength, and ‘θ’ is the angle between the plane of the coil and the direction of the magnetic field.

Since the magnetic field is radial, θ changes as the coil rotates. However, if we assume that θ is small, we can approximate sin θ by θ itself. Thus, we get-

The spring or strip attached to the coil produces a counter torque that opposes the rotation of the coil. The counter torque is given by:

where ' is the counter torque and ‘k’ is the spring or strip constant.

When the coil reaches an equilibrium position, where it stops rotating, its net torque becomes zero. Thus, we have:

Or,

Solving the above equation, we will get:

This shows that:

The pointer or mirror attached to the coil indicates the value of θ on a scale. Thus, by knowing the values of k, n, B, and A, we can measure the value of I.

Sensitivity of Moving Coil Galvanometer

The sensitivity of a moving coil galvanometer is defined as the deflection angle's ratio to the coil's current. It measures how much the coil deflects for a given current. Mathematically, it can be expressed as follows:

where S is the sensitivity, θ is the deflection angle, and I is the current in the coil.

Using the formula for ‘I’ derived earlier, we can write:

This shows that S is proportional to n, B, and A and inversely proportional to k.

Therefore, to increase the sensitivity of the moving coil galvanometer, we can:

Increase the number of turns in the coil
Increase the strength of the magnetic field
Increase the area of the coil
Decrease the spring or strip constant

Conversion of the Galvanometer to Ammeter

An ammeter is an instrument that measures electric current in a circuit. To convert a galvanometer into an ammeter, we need to connect a low resistance called a shunt in parallel with it. The shunt allows most of the current to bypass the galvanometer and only a small fraction of the current to pass through it. This prevents the galvanometer from being overloaded or damaged by high currents.

The diagram of a galvanometer converted into an ammeter is shown below:

To calculate the value of the shunt resistance, we can use the following formula:

where S is the shunt resistance, G is the galvanometer resistance, ig is the galvanometer current, i is the current in the ammeter, and it is the shunt current.

Conversion of Galvanometer to Voltmeter

A voltmeter is an instrument that measures the electric potential difference or voltage across two points in a circuit. To convert a galvanometer into a voltmeter, we need to connect a high resistance called a multiplier in series with it. The multiplier increases the resistance of the galvanometer and reduces the current flowing through it. This allows the galvanometer to measure high voltages without being affected by them.

The diagram of a galvanometer converted into a voltmeter is shown below:

To calculate the value of the multiplier resistance, we can use the following formula:

where M is the multiplier resistance, V is the full-scale deflection voltage of the voltmeter, G is the galvanometer resistance, and i_g is the full-scale deflection current of the galvanometer.

Solved Problem

Q1. A moving coil galvanometer of resistance 100Ω is used as an ammeter using a resistance of 0.1Ω. The maximum deflection current in the galvanometer is 100μA. Find the current in the circuit so that the ammeter shows maximum deflection. (IIT JEE 2005)

Solution:

It is given that G = 100Ω, S = 0.1Ω, i_g = 100μA

We know that,

Arranging the equation further:

Putting the values in the equation:

Solving, we get:

Practice Problem

Q1. A galvanometer coil of 30Ω resistance shows full range deflection for a current of 5mA. What will be the voltage displayed on the voltmeter if the multimeter resistance is given as 36.667Ω?

Frequently Asked Questions

Q1. What is a galvanometer used for?
Answer: A galvanometer is a device that is used to detect a small electric current or measure its magnitude.

Q2. What are the different types of galvanometers?
Answer: One type of galvanometer is the moving coil galvanometer. Other than that, there is the tangent galvanometer, astatic galvanometer, mirror galvanometer, ballistic galvanometer, etc.

Q3. What is the difference between a galvanometer and a galvanoscope?
Answer: A galvanometer is an instrument that can measure the magnitude of a small electric current by indicating the deflection of a magnetic needle or a coil in a magnetic field. A galvanoscope is an instrument that can only detect the presence or absence of a small electric current by showing whether the magnetic needle or coil moves or not. A galvanoscope is a simpler and less sensitive version of a galvanometer.