Direct Energy, 2018a

48 2.4 Problems
2.5. A piezoelectric material has a permittivity of ɛ =3.54 · 10 −11 m F and
has a piezoelectric strain constant of d =2· 10 −10 m V
. If the material
is placed in an electric eld of strength | −→ E | =70 m V and is subjected
to a stress of | −→ ς | =3.5 m N . Calculate the material polarization.
2
2.6. A piezoelectric material has permittivity ɛ r =2.5. If the material is
placed in an electric eld of strength | −→ E | =2·10 3 m V and is subjected
to a stress of | −→ ς | = 200 m N , the material polarization of the material
2
is 3.2 · 10 −8
m C . Calculate d, the piezoelectric strain constant.
2
2.7. Consider two piezoelectric devices of the same size and shape. The
dielectric material of the rst device has a permittivity of ɛ =2.21 ·
10 −11 F m and a piezoelectric strain constant of d =8· 10−11 m V . The
dielectric material of the second device has an electric susceptibility
of χ e =3.2 and a piezoelectric strain constant of d =2· 10 −10 m V .
(a) Find ɛ r , the relative permittivity, for each device.
(b) Find C 1
C 2
, the ratio of the capacitance of the rst device to the
capacitance of the second device.
(c) The devices are placed in an external electric eld of strength
| −→ E| =32 V m . No stress is placed on the devices. Calculate the
material polarization, −→ P for each device.
(d) The devices are placed in an external electric eld of strength
| −→ E| =32 V m , and a stress of |−→ ς | = 100 m N is applied to the
2
devices. Calculate the material polarization, −→ P for each device.
(e) Which device would you expect is able to store more energy?
Explain your answer.
2.8. A particular piezoelectric device has a cross sectional area of 10 −5 m 2 .
When a stress of 800 m N is applied, the device compresses by 10 μm.
2
Under these conditions, the device can generate 2.4·10 −9 J. Calculate
the eciency of the device.
2.9. A particular piezoelectric device has a cross sectional area of 10 −5 m 2
and an eciency of 5%. When a stress of 1640 m N is applied to the
2
device, it oscillates with an average velocity of 0.01 m s . Calculate the
power that can be generated from the device.