Question

Write the definition of figure of merit of Galvanometer.

Answer 1

Hint: The figure of merit in general is defined as the numerical value representing the degree of effectiveness or efficiency of an instrument approximated by different estimation techniques. Galvanometer is a device which is used to measure small electric current. When current passes through the coil of the galvanometer, a deflection is observed. Use this information to find the definition of figure of merit of Galvanometer.

Complete answer:

Galvanometer is a device used to detect feeble electric voltage and current in a circuit. The figure of merit of a galvanometer can be defined as a current required to produce unit deflection in the galvanometer scale. The figure of merit is denoted by the symbol k. It is given by,
$k={\displaystyle \frac{I}{\theta }}$ …(1)
Where, I is the current through the coil
            $\theta$ is the angle of deflection
At equilibrium,
$I=\left({\displaystyle \frac{K}{NAB}}\right)\theta$ …(2)
Where, K is the restoring torque per unit twist of spring constant
             N is the number of turns in the coil
             A is the area of the galvanometer coil
             B is the magnetic flux density of the radial magnetic field of galvanometer magnet
Substituting equation. (2) in equation. (1) we get,
$k={\displaystyle \frac{\left({\displaystyle \frac{K}{NAB}}\right)\theta }{\theta }}$
$\Rightarrow k={\displaystyle \frac{K}{NAB}}$ …(3)
But, $G={\displaystyle \frac{k}{NAB}}$ ...(4)
Where, G is the galvanometer constant
From the equation. (2) and (3) we get,
$k=G$

Note:
Galvanometer has a moderate resistance of about $100\mathrm{\Omega }$ and the galvanometer itself has a small current carrying capacity of 1 mA. The deflection in the galvanometer is directly proportional to the current passed through it. Students must remember that a galvanometer can be used as an ammeter as well as a voltmeter. If we want to use it as an ammeter then it should be connected along the element. Whereas if we have to use a galvanometer as a voltmeter then it should be connected across the element.