In a moving coil galvanometer, torque on the coil can be expressed as $τ = k i$ , where i is current through the wire and k is constant. The rectangular coil of the galvanometer having number of turns N, area A and moment of inertia I is placed in magnetic field B and is suspended by a string with a certain torsional constant

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The maximum angle through which coil is deflected if charge Q is passed through the coil almost instantaneously is $Q \sqrt{\frac{N A B π}{2 I i_{0}}}$ (Ignore the damping in mechanical oscillations , use same torsional constant related to data in option “B” )

Value of constant k is NAB

The maximum angle through which coil is deflected if charge Q is passed through the coil almost instantaneously is $Q \sqrt{\frac{2 N A B π}{I i_{0}}}$ (Ignore the damping in mechanical oscillations , use same torsional constant related to data in option “B”)

The torsional constant of the string , if a current $i_{0}$ produces a deflection of $\frac{π}{2}$ in the coil in reaching equilibrium position is $\frac{2 N i_{0} A B}{π}$

answer is A, B, C.

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Detailed Solution

At equilibrium restoring torque $C θ = N i A B, C i s t o r s i o n a l c o n s \tan t$
$\int N i A B d t = I ω, ω = \frac{N A B Q}{I}$ At maximum deflection $\frac{1}{2} I ω^{2} = \frac{1}{2} C {θ_{0}}^{2}$