For some purposes (such as measuring quantity of electricity rather than current) galvanometers are designed with the moving coil having a large moment of inertia and a long period. This enables a small quantity of electricity to be discharged through the galvanometer in a time that is small in comparison with the period of the galvanometer. Under these circumstance a deflection is obtained that is proportional to the charge. This follows from the fact that the angular momentum Iω imparted to the coil is given by
When I the moment of inertia of the coil is ω is the angular speed imported to it, L is the torque produced by the current i, K is a constant, and Q is the total charge sent through the coil. As a result of its angular momentum the coil deflects until its kinetic energy of rotation is transferred into the potential energy of the twisted suspension. The deflection s thus produced is therefore proportional to the charge, or
The kb is known as the ballistic constant of the galvanometer. Ballistic galvanometers are useful for the comparison of capacitors.
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