   # The ballistic galvanometer When a pulse of current passes through a moving coil instrument the coil is given an impulse which sets is swinging. If the duration of the pulse is short compared with the natural period of oscillation of the coil (T), then the amplitude of the oscillation does not depend on the way in which the current varies during the pulse. Such an instrument therefore uses a heavy coil wound on an insulating former giving little or no damping. The mass of the coil gives it a large moment of inertia and therefore makes it swing slowly.

If the duration of current is small compared with T, then it can be shown that the first deflection is directly proportional to the charge passed, that is, Q = kq1. (k is a constant for the particular suspension).

In fact,

q1 = [2nS/T]Q where S is the sensitivity of the instrument, BAN/k.

After the pulse has passed through it the motion of the coil depends on
(a) the restoring couple due to the suspension,
(b) the damping due to air currents and any eddy currents in the circuit.
The coil therefore oscillates with an exponential decrease of amplitude, as shown in the diagram.
For the Pye spot galvanometer T = 2s, the instrument is critically damped for an external resistance of 100 W. A 1 mm deflection is obtained for about 10-8C.

The ballistic galvanometer may be calibrated using:
(a) a standard capacitor,
(b) a standard mutual inductor.

The ballistic galvanometer may be used to compare or to determine the value of either capacitors or magnetic fields.