Question

In a tangent galvanometer a current of 0.1A produces a deflection of \[{30^0}\]. Find the current required to produce a deflection of \[{60^0}\] .
A. 0.2A
B. 0.3A
C. 0.4A
D. 0.5A

Answer 1

Hint:Before we start addressing the problem, we need to know the data provided. Here we have the deflections produced and a current through the tangent galvanometer. Using this we are going to find the current required to produce a deflection of \[{60^0}\]. A tangent galvanometer is defined as a type of galvanometer that has a vertical coil of wire with a horizontal magnetic needle at its centre and measures the current.

Formula Used:
The formula to find the current through the tangent galvanometer is given by,,
\[i = K\tan \theta \]……. (1)
Where,
K is a reduction factor.
\[\theta \] is the deflection of the needle.

Complete step by step solution:
The current through the tangent galvanometer is given by equation (1) that is,
\[i = K\tan \theta \]
From the above equation, we obtain,
\[\dfrac{{{i_1}}}{{{i_2}}} = \dfrac{{\tan {\theta _1}}}{{\tan {\theta _2}}}\]
\[\Rightarrow \dfrac{{0.1}}{{{i_2}}} = \dfrac{{\tan {{30}^0}}}{{\tan {{60}^0}}}\]
By data, \[{i_1} = 0.1A\]
\[{i_2} = \dfrac{{0.1 \times \tan {{60}^0}}}{{\tan {{30}^0}}}\]
Substituting the value of \[\tan {60^0}\]and \[\tan {30^0}\]in above equation we get,
\[{i_2} = \dfrac{{0.1 \times \sqrt 3 }}{{\left( {\dfrac{1}{{\sqrt 3 }}} \right)}}\]
\[ \therefore {i_2} = 0.3A\]
Therefore, the current required to produce a deflection of \[{60^0}\] is 0.3 A.

Hence, Option B is the correct answer

Note:Reduction factor of a tangent galvanometer is defined as the amount of current which is required to produce a deflection of \[{45^0}\]. The tangent galvanometer works on tangent law and the current through the coil is directly proportional to the tangent of the angle of deflection of the needle. The tangent galvanometer has a non-linear scale and is affected by the external magnetic field. When compared to a moving coil galvanometer the tangent galvanometer is less sensitive.