Question

A tangent galvanometer shows a deflection ${45}^{\circ }$ when $10mA$ current passes through it. If the horizontal component of the earth’s field is $3.6\times {10}^{-5}T$ and radius of the coil is $10cm$. The number in the coil is

• A. $57$ turns
• B. $5.7$ turns
• C. $5700$ turns
• D. $570$ turns

Answer 1

The correct option is D $570$ turns

reading of tangent galvanometer
for a tangent galvanometer, if deflection $=\theta$, the current reading is given by

$i=ktan\theta$

where, $k=\frac{2r{B}_H}{{\mu }_{0}n}$= reduction factor of
galvanometer

$(n$ no. of turns in the coil, 𝑟= radius of the coil)

$i=\frac{2r{B}_H}{{\mu }_{0}n}tan\theta$

$n=(\frac{2r{B}_H}{{\mu }_{0}i}tan\theta$

$=\frac{\left(2\right)\left(0.1m\right)(3.6\times {10}^{-5}T)}{(4\pi \times {10}^{-7})\left({10}^{-2}A\right)}tan{45}^{\circ }$

$=\frac{1.8\times {10}^3}{3.14}\approx 570$

Hence, the correct option is (c)