A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for \(\frac{1}{3}\) deflection in the galvanometer. Which of the below is true for measuring the value of G?

CONCEPT:

The galvanometer is a sensitive device used to detect very low currents in the device. Its working is based on the principle in which a coil placed in a uniform magnetic field experiences a torque when an electric current is set up in it. The deflection of the coil is determined by a pointer attached to it, moving on the scale.

CALCULATION:

It is given that a teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. The circuit is shown below;

We can see that G and S are parallel to each other, therefore, 

(I - I_g) S = I_gG

IS - I_g S = I_g G

⇒ IS = Ig G + Ig S

⇒ IS = (G+S) I_g 

⇒ \(\frac{I}{I_g}= \frac{G+S}{S}\) 

⇒ \(\frac{I_g}{I}= \frac{S}{G+S}\) ------(1)

Now, a student took observations and gets a deflection of 1/3, therefore equation (1) becomes;

⇒ \(\frac{1}{3}= \frac{S}{G+S}\) 

⇒ G+S = 3S

⇒ G = 2S

Therefore, the 1/3 deflection method can be used and in this case, the G equals twice the value of shunt resistance(S).

Hence option 2) is the correct answer.