Conversely, if we take the same slab, attach a battery and charge it, part of the input energy will be transduced to mechanical energy and will deform the slab, making it smaller or larger, dependent on the polarity of the battery.
The same relationship holds, and the coupling coefficient is numerically identical:
k 2 = electrical energy converted to mechanical energy input electrical energy
The dielectric constant measures the amount of charge that an electroded slab of material can store, relative to the charge that would be stored by identical electrodes separated by air or vacuum at the same voltage.
If we measure the dielectric constant of a piezoelectric material, first without applied stress, and then clamped mechanically so firmly that it cannot deform, the same numerical value of coupling coefficient can be found:
This method is actually used by first measuring the dielectric constant at low frequency, where the slab is free to vibrate, and then measuring at high frequency, above all the mechanical resonances, where the slab crystals effectively clamped by its own inertia.