Problem 1
A parallel plate capacitor has a capacitance of \(C=10 \mathrm{pF}\). The plates have area \(0.025 \mathrm{~cm}^{2}\). A dielectric layer of thickness \(d_{\text {thick }}=0.01 \mathrm{~mm}\) separates the plates. For the dielectric layer, calculate the permittivity \(\epsilon,\) the relative permittivity \(\epsilon_{r},\) and the electric susceptibility \(\chi_{e}\)
Problem 3
A cylindrical sandwich cookie has a radius of 0.75 in. The cookie is made from two wafers, each of thickness 0.15 in, which are perfect dielectrics of relative permittivity \(\epsilon_{r}=2.8 .\) Between the wafers is a layer of cream filling of thickness 0.1 in which is a perfect dielectric of relative permittivity \(\epsilon_{r}=2.2 .\) Find the overall capacitance of the cookie. Hint: Capacitances in series combine as \(\frac{1}{\frac{1}{C_{1}}+\frac{1}{C_{2}}}\).
Problem 4
A parallel plate capacitor has a capacitance of \(3 \mu \mathrm{F}\). (a) Suppose another capacitor is made using the same dielectric material and with the same cross sectional area. However, the thickness of the dielectric between the plates of the capacitor is double that of the original capacitor. What is its capacitance? (b) Suppose a third capacitor is made with the same cross sectional area and thickness as the first capacitor, but from a material with twice the permittivity. What is its capacitance?
Problem 6
A piezoelectric material has permittivity \(\epsilon_{r}=2.5 .\) If the material is placed in an electric field of strength \(|\vec{E}|=2 \cdot 10^{3} \frac{\mathrm{V}}{\mathrm{m}}\) and is subjected to a stress of \(|\vec{\zeta}|=200 \frac{\mathrm{N}}{\mathrm{m}^{2}},\) the material polarization of the material is \(3.2 \cdot 10^{-8} \frac{\mathrm{C}}{\mathrm{m}^{2}} .\) Calculate \(d,\) the piezoelectric strain constant.
Problem 8
A particular piezoelectric device has a cross sectional area of \(10^{-5} \mathrm{~m}^{2}\). When a stress of \(800 \frac{\mathrm{N}}{\mathrm{m}^{2}}\) is applied, the device compresses by \(10 \mu \mathrm{m}\). Under these conditions, the device can generate \(2.4 \cdot 10^{-9} \mathrm{~J} .\) Calculate the efficiency of the device.
Problem 9
A particular piezoelectric device has a cross sectional area of \(10^{-5} \mathrm{~m}^{2}\) and an efficiency of \(5 \% .\) When a stress of \(1640 \frac{\mathrm{N}}{\mathrm{m}^{2}}\) is applied to the device, it oscillates with an average velocity of \(0.01 \frac{\mathrm{m}}{\mathrm{s}} .\) Calculate the power that can be generated from the device.
Problem 11
According to the data sheet, a piezoelectric device is \(3 \%\) efficient. A coworker says that energy is not conserved in the device because \(97 \%\) of the energy is lost when it is used. Explain what is wrong with your coworker's explanation.
