Question

The number of turns and radius of cross-section of the coil of a tangent galvanometer are doubled, the reduction factor $\mathrm{K}$ will be :
A. remain same
B. be doubled
C. be quadrupled
D. be one fourth

Answer 1

Hint: An early measuring tool for measuring electric current is a tangent galvanometer. It operates by comparing the magnetic field produced by an unknown current to the magnetic field of the Earth using a compass needle. Current steadiness is measured using a tangent galvanometer.

Complete step by step solution:
We know that $i=\dfrac{2 \gamma B_{H}}{M_{0} n} \tan \theta$
$B_{H}=$ horizontal component
$\tan \theta=$ Angle of deflection
and we know that
$i=k \tan \theta$
A tangent galvanometer's reduction factor is measured in amperes. The tangent of the angle of the compass needle in a galvanometer is proportional to the relative strength of the two perpendicular magnetic fields, according to the tangent law of magnetism.
$K^{\prime} \rightarrow$ new reduction factor
$k^{\prime}=\dfrac{2 \times 2 \gamma \times B_{H}}{\mu_{0} \times 2 n}=k$
The new reduction factor, $k=k$
It remains same

Hence, the correct answer is option A.

Note: Tangent galvanometer is a device used for estimating current, and it is used to measure steady flows. It lowers the bar set by Tangent law. A beautiful needle strung at a location where two crossed fields are in right angles to one another will stop moving in the direction of the result of the two fields.
The magnetic field of Earth immediately causes the instrument needle to start moving.
Development continues until the plane of the loop and the earth's attractive field are aligned.
At that time, a second attractive field on the pivot of the loop that is opposed to the attractive field of the Earth is created using an unknown current.
As a result, the vector sum of the two fields triggers a response from the compass needle.