Question

To know the resistance $G$ of a galvanometer by half deflection method, a battery of $emf\,{V_E}$ and resistance $R$ is used to deflect the galvanometer by angle$\theta $ . If a shunt of resistance $S$ is needed to get half deflection then $G,R\,\,and\,S$ are related by the equation
A.$2S = G$
B.$S\left( {R + G} \right) = RG$
C.$2S\left( {R + G} \right) = RG$
D.$2G = S$

Answer 1

Hint: To solve this problem, firstly we should understand about the Galvanometer, its principle, its application and the concept behind it. We will also study the shunt resistor and all the related information. And by using these concepts we can easily approach our answer.

Complete answer:
The galvanometer is an instrument used for the detecting presence of small amounts of current and voltage or for determining their magnitude. The galvanometer works in the principle where potentiometers indicate the null deflection or zero current.
 The potentiometer based on the current endure coil is kept between the magnetic field experiences a torque. The galvanometer has various applications, it is used for detecting the direction of current flows in the circuit. It is used for detecting current, the voltage between any two points of the circuit is also determined through a galvanometer.
Shunt Resistor: Resistor having a low value of resistance such type of resistor is called shunt resistance. The shunt resistor is consisting of the material having the low- temperature coefficient of resistance. It is connected with the ammeter when connected in parallel whose range is to be extended. It is connected in series with the load in it whose current is to be measured.

After applying shunt $S$ , deflection gets halved,
Hence, the current gets halved.

Hence,
$\dfrac{1}{2}\,\dfrac{V}{{R + G}} = \dfrac{V}{{R + \dfrac{{GS}}{{G + S}}}}\,\dfrac{S}{{G + S}} = \dfrac{{VS}}{{GS + RG + RS}}$

We get,
$S\left( {R + G} \right) = RG$

So, the correct answer of this problem is option B - $S\left( {R + G} \right) = RG$

Note: Instrument used for measuring and indicating an electric current is known as galvanometer. The galvanometer has various applications, it is used for detecting the direction of current flows in the circuit. It is yielded for measuring the current, the voltage between any two points of the circuit is also detected through the galvanometer.