Question

What is a galvanometer? Describe the construction and working of a galvanometer using a labelled diagram.

Accepted Answer

A moving coil galvanometer is an instrument used to detect and measure small electric currents. It works on the principle that a current carrying coil in a magnetic field experiences a torque.

Construction of the galvanometer:

A moving coil galvanometer consists of a coil $P Q R S_{1}$ having a large number of turns of insulated copper wire. The coil is wound over a non-magnetic metallic frame. The coil is suspended from a movable torsion head $H$ by means of phosphor bronze strip in a uniform magnetic field produced by two strong cylindrical magnetic pole pieces. This is done so that the magnetic field linked with the coil is a radial field, i.e., the plane of the coil in all positions remain parallel to the direction of the magnetic field.

The lower end of the coil is connected to one end of a hair spring $S'$ of phosphor bronze. The other end of this highly elastic spring is connected to the terminal $T_{2}$ . A soft iron core is placed within the coil to increase the strength of the magnetic field. $M$ is a mirror attached to phosphor bronze strip to note the deflection of the coil using lamp and scale arrangement. The torsion head is connected to the terminal $T_{1}$ .

Working of galvanometer:
A coil of $N$ turns, area $A$ and a current $I$ when placed in a magnetic field, experiences a torque, given by $τ_{d e f} = N A I B \sin θ$

Since the magnetic field is radial $θ = 90 °$ . Therefore,
$τ_{d e f} = N A I B \sin 90 ° = N A I B$

Due to this torque, the coil rotates and the phosphor bronze strip gets twisted. As a result, a restoring torque is produced by the strip which tends to restore the coil back to its original position. Let $ϕ$ be the twist produced in the phosphor bronze strip and $C$ be the restoring torque per unit twist. Then the restoring torque is

$τ_{R} = C ϕ$

In equilibrium, $τ_{d e f} = τ_{R}$

$N A I B = C ϕ$

$I = (\frac{C}{N A B}) ϕ$

$I = k ϕ$

where $k = \frac{C}{N A B}$ ; $k$ is a constant called reduction factor of the galvanometer.

Hence $I \propto ϕ$

The deflection is measured using lamp and scale arrangement. If the perpendicular distance of the mirror from the scale is $D$ and the deflection of the light spot on scale is $d$ .

$\tan (2 ϕ) = \frac{d}{D}$
For small deflection, $2 ϕ = \frac{d}{D}$

$ϕ = \frac{d}{2 D}$

$∴ I \propto d \propto ϕ$

What is a galvanometer? Describe the construction and working of a galvanometer using a labelled diagram.

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