Question

Two galvanometers A and B require 3mA and 6mA respectively, to produce the same deflection of 10 divisions. Then is,
A. A is more sensitive that B
B. B is more sensitive than A
C. A and B are equally sensitive
D. Sensitiveness of B is twice that of A

Answer 1

Hint:In order to solve this question we need to remember that in these cases where the deflection comes out to be equal in two cases the sensitivity of the galvanometer is directly proportional to the current through it.

Complete step by step solution:
Sensitivity, a term used to define how effectively any substance responds to any action. Substance in less action, give more reaction is a sensitive one. In the given question we need to determine the sensitivity of two galvanometers A and B. In the given question we need to find which is more sensitive galvanometer in deflection of core to 10 division (which one gives this reaction fast).

It is given in the question that the Galvanometer A needs only 3mA current to show 10 divisions whereas galvanometer B shows deflection on the action of 6mA current. From this we can conclude that galvanometer A is more sensitive than galvanometer B because galvanometer reacting (deflected through 10 division) only by action of 3mA current as compared to galvanometer B.

Mathematically sensitivity (\[{{S}_{A}}\] and \[{{S}_{B}}\]) is defined as the ratio of number of division by per unit current thus,
${{S}_{A}}=n/I$ and ${{S}_{B}}=n/I$
$\Rightarrow {{S}_{A}}=10/3$,
And
${{S}_{B}}=10/6$
The sensitivity ratio of A and B is given by,
$\dfrac{{{S}_{A}}}{{{S}_{B}}}=\dfrac{{{I}_{B}}}{{{I}_{A}}}$
$\Rightarrow \dfrac{{{S}_{A}}}{{{S}_{B}}}=\dfrac{6}{3}$
$\therefore {{S}_{A}}>{{S}_{B}}$
Thus, galvanometer A is more sensitive than galvanometer B.

Hence, option A is the correct answer.

Note: Galvanometer is the name of the instrument used to measure tiny electric currents. Or, to put it another way, we may say that the Galvanometer is employed to gauge the strength of an electric current. The magnetic needle's movement provides information about the current. This device's magnetic field coil is an essential component.