State the principle of moving coil galvanometer. Explain its working and obtain the expression for the deflection produced due to current passed through the coil. Define the current sensitivity.

When a current carrying coil is placed in a magnetic field, its experiences a torque which causes a coil to rotate at a certain angle.

When the current is passed through the coil, it experiences a torque which expressed as;

$\tau = NIAB \sin \theta$

where,

N = number of turns

A = area

B = magnetic field

I = current

$\tau = NIAB \sin \theta$            $(\because \sin \theta = 90^{\circ})$

then,

$\tau = NIAB$

then,

Restoring torque $\tau ^{'}= k\phi$

at equilibrium,

$\tau = \tau ^{'}$

$\therefore NIAB = k\phi$

$\phi = \left [ \frac{NAB}{k} \right ]I$

$\frac{\phi}{I}= \frac{NAB}{k}$  is the current sensitivity.

Current sensitivity is defined as the deflection per unit current.

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