Question

What is the relation between figure of merit \((\mathrm{k})\) and current sensitivity \(\left(\mathrm{S}_{1}\right) ?\) (A) \(\mathrm{S}_{1}=\mathrm{k}^{-1}\) (B) \(\mathrm{S}_{1}=(\mathrm{k} / 2)\) (C) \(\mathrm{S}_{1}=\mathrm{kV}\) (D) \(\mathrm{S}_{1}=(\mathrm{k}) \mathrm{I}\)

Short answer

(A) \(S1=k^{-1}\)

Step-by-step solution

Understand Figure of Merit (k)

The figure of merit (k) is a dimensionless quantity that shows the performance of a measuring instrument such as a galvanometer. The figure of merit represents the inverse of the amount of magnetic field required for a measuring instrument to deflect per unit current.

Understand Current Sensitivity (S1)

Current sensitivity (S1) refers to the deflection produced in an instrument when a unit current flows through it. Essentially, it tells us how sensitive an instrument is to the change in current.

Find the Relationship between k and S1

Since the figure of merit (k) represents the inverse of the amount of magnetic field required for an instrument to deflect per unit current, and current sensitivity (S1) represents the deflection produced in an instrument when a unit current flows through it, we can say that: \(S1 = k^{-1}\) Therefore, the correct answer is: (A) \(S1=k^{-1}\)