Moving Coil Galvanometer

A moving coil galvanometer is a tool designed to detect and measure small electric currents. It operates on the principle that when a current flows through a coil placed in a magnetic field, it experiences a torque, causing the coil to rotate. The device features a lightweight coil suspended between the poles of a magnet, and as the current passes through, the coil rotates, causing a needle to move across a scale, indicating the current level. The sensitivity of the galvanometer is influenced by factors such as the number of turns in the coil, the strength of the magnetic field, and the quality of the suspension. There are two main types of galvanometers: suspended and pivoted. This instrument serves as the foundation for creating ammeters and voltmeters.

1.0Basics of Moving Coil Galvanometer

• It is a device used to detect current in a circuit. The widely used moving coil galvanometer is named for its design, which features a current-carrying coil that rotates within a magnetic field as a result of the torque acting upon it.

2.0Principle and Types of Moving Coil Galvanometer

Principle:A coil carrying current, when placed in a magnetic field, experiences a torque that depends on the magnitude of the current. This torque causes the coil to rotate, resulting in an angular deflection.

Types of Moving Coil Galvanometer

3.0Construction of Moving Coil Galvanometer

• The galvanometer is made up of a multi-turn coil that can freely rotate around a fixed axis within a uniform radial magnetic field. A cylindrical soft iron core is placed at the center, which not only helps to maintain the radial nature of the field but also enhances its strength. Additionally, a spiral spring is connected to the coil, providing a restoring torque that opposes its rotation.
• A cylindrical soft iron core is mounted symmetrically between the concave poles of the horse-shoe magnet.This makes the lines of force pointing along the radii of a circle.Such a field is called a radial field.
• The plane of a rotating coil in such a magnetic field stays parallel to the field at all times. Additionally, the soft iron cylinder, owing to its high magnetic permeability, strengthens the magnetic field and thereby enhances the sensitivity of the galvanometer.
• If the radial field were not present in a moving coil galvanometer the scale would then be non-linear and difficult to calibrate or to be read accurately.
• Phosphor -bronze is used for suspension or hair springs because of several reasons,good conductor of electricity,does not oxidise,perfectly elastic,very little elastic after effect,non-magnetic,it has minimum value for restoring torque per unit twist i.e. smallest torsion constant k.

4.0Working of Moving Coil Galvanometer

Working Principle:When a current-carrying coil is placed in a magnetic field, it experiences torque due to the interaction between its own magnetic field and the external one. Opposite sides of the coil face equal and opposite forces, causing it to rotate about its axis.

$$\begin{gathered} \mathbf{\tau }=NI(\mathbf{A}\times \mathbf{B}) \\ \tau =NIAB\sin \theta \\ \tau =NIAB(\theta =90^{\circ }\text{ due to radial magnetic field}) \\ I=\text{current through coil} \\ A=\text{Area of coil} \\ B=\text{Magnetic field} \\ N=\text{no. of turns} \end{gathered}$$

This torque tends to rotate the coil by $\varphi$ angle.The spring S provides a counter torque C $\varphi$ that balances the magnetic torque. In equilibrium,

$$\begin{gathered} C\varphi =NIAB \\ I=\frac{C}{NAB}\varphi \Rightarrow I\propto \varphi \end{gathered}$$

Galvanometer Constant

 $G=\frac{C}{NAB}$, is constant for galvanometer and is called Galvanometer Constant or Current Reduction Factor of the Galvanometer

Hence, it means the deflection produced is proportional to the current flowing through the galvanometer.

Figure of Merit of Galvanometer: It is defined as the current which produces a deflection of one scale division in the galvanometer and is given by,

$G=\frac{I}{\varphi }=\frac{C}{NAB}$

5.0Sensitivity of Galvanometer

1. Current Sensitivity: Current sensitivity is defined as the deflection created in the galvanometer when a unit current flows through it.

$C\cdot S=\frac{\varphi }{I}=\frac{NAB}{C}(\text{rad/A})$

2.Voltage Sensitivity: Voltage sensitivity is equal to the deflection per unit voltage applied across voltmeters.

$V.S=\frac{\varphi }{V}=\frac{\varphi }{IR}=\frac{NAB}{CR}(\text{rad/V})$

6.0Advantages And Disadvantages of Moving Coil Galvanometer

Advantage of a Moving Coil Galvanometer

1. Linear scale due to deflection being proportional to current.

2.High sensitivity achievable by optimizing design factors (N, B, A, C).

3.Strong magnetic field shields from external interference.

4.Metallic frame induces eddy currents for quick damping.

Disadvantage of a Moving Coil Galvanometer

1.Sensitivity cannot be adjusted easily.

2.Susceptible to damage from overload (e.g., spring burnout).

7.0Conversion of Galvanometer into Ammeter

• To convert a galvanometer into an ammeter a very small resistance is connected in parallel to the galvanometer called SHUNT.
• Resistance of an ammeter is very small and it is zero for ideal ammeter i.e. ideal ammeter behaves like conducting wire.
• Value of shunt.

$$\begin{gathered} V_s=V_G\Rightarrow (i-i_g)S=i_{g}G \\ \Rightarrow S=\left(\frac{i_g}{i-i_g}\right)G \\ \Rightarrow S=\left(\frac{1}{\frac{i}{i_g}-1}\right)G\Rightarrow S=\left(\frac{G}{n-1}\right)\text{where}n=\frac{i}{i_g}\text{G}--resistanceofgalvanometer \\ {i}_g--\text{range of galvanometer or current required to produce full deflection} \\ \text{i}--\text{Range of ammeter (Max. current can be measured.)} \end{gathered}$$

NOTE:

1.To increase the range of an ammeter, a shunt is joined in parallel with the galvanometer.

2. To convert an ammeter of range I I amperes and resistance $R_g\Omega$ into an ammeter of range nI amperes, the value of resistance to be connected in parallel will be $\frac{R_g}{n-1}\Omega$

3.Resistance of ideal ammeter is zero. 

8.0Conversion of Galvanometer into Voltmeter

• To transform a galvanometer into a voltmeter capable of measuring higher potential differences, a high-value resistor is connected in series with the galvanometer. 
• The resistance of the voltmeter is very high and it is infinite for an ideal voltmeter.
•  So ideal voltmeter open circuit

Resistance R and G+H (G+H) are in parallel between points A and B ,it may be represented as,

$$\begin{gathered} i_g(G+H)=(i-i_g)R \\ iG+iH=(i-i_g)R \\ {V}_g+V_H=V\Rightarrow V_H=V-V_g \\ {V}_H=V-V_g \\ iH=V-V_g \\ \frac{V_g}{G}H=V-V_g \\ {V}_{g}H=(V-V_g)G \\ H=\left(\frac{V-V_g}{V_g}\right)G=\left(\frac{V}{V_g}-1\right)G \\ H=(n-1)G\text{where}n=\frac{V}{V_g} \end{gathered}$$

NOTE:

1.To extend the measuring range of a voltmeter, a high-value resistor is connected in series with the instrument.

2. To convert a voltmeter of resistance $R_g\Omega$ and range V volts into a voltmeter of range nV volts, the value of resistance to be connected in series will be $(n-1)R_g\Omega$

3. Resistance of the ideal voltmeter is infinite.