Name: Working of Galvanometer
Uploaded: 2019-07-19
Duration: 9 min 22 s
Description: A galvanometer is a device used to indicate the presence, direction or strength of a small electric current. Let's study the working principle and applicatio...

Question

Explain the working of a moving coil galvanometer. How it can be converted into ammeter?

Accepted Answer

Principle of moving coil galvanometer: when a current-carrying coil which is suspended freely in a magnetic field, a torque acts upon the coil and due to this torque, the coil rotates and the deflection of the coil is directly proportional to the current flowing through the coil.

Let us first consider a single turn $ABCD$ of the rectangular coil having a length $l$ and breadth $b$ This is suspended in a magnetic field of strength $B$ such that the plane of the coil is parallel to the magnetic field. Since the sides $AB and DC$ are parallel to the direction of the magnetic field, they do not experience any effective force due to the magnetic field. The sides $AD, BC$ being perpendicular to the direction of field experience an effective force given by $F = BIl$

Using Fleming’s left-hand rule we can determine that the forces on $AD and BC$ are in opposite directions to each other. When equal and opposite forces act on the coil, it produces a torque. This torque causes the coil to deflect.

The torque τ = force x perpendicular distance between the forces

Torque τ acting on single-loop $ABCD$ of the coil = $τ = BI l \times b = NlAB$

Where $l \times b = area A$ and $N$ = the number of coils.

The magnetic torque thus produced causes the coil to rotate, and the phosphor bronze strip twists. In turn, the spring S attached to the coil produces a counter torque or restoring torque $k θ$ which results in a steady angular deflection

Under equilibrium condition:

$kθ = NIAB$ ,Here $k$ is called the torsional constant of the spring (restoring couple per unit twist). The deflection or twist θ is measured as the value indicated on a scale by a pointer which is connected to the suspension wire.

$θ = (\frac{NAB}{k}) l$ or $I = \frac{k}{NAB} θ$

This is the required expression.

Hence, the deflection that occurs in the galvanometer is directly proportional to the current that flows through it

Conversion into an ammeter:

A galvanometer can detect only small currents. Thus, to measure large currents it is converted into an ammeter. It can be converted into an ammeter by connecting a low resistance called shunt resistance in parallel to the galvanometer.

Let $G$ is the resistance of the galvanometer and ' $S$ is the low resistance connected in parallel. Since ' $G and S$ are in parallel so, potential difference across them will be the same. Let $I$ be the total current out of which $I_{g}$ passes through the galvanometer, therefore we have,

$I_{g} \times G = (I - I_{g}) S$ .

Or $\frac{I_{g}}{I} = \frac{S}{S + G} or S = \frac{I_{g} G}{I - I_{g}}$ .

This is the required value of shunt resistance to convert a galvanometer in to ammeter to measure a current $I_{g}$ .

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