Answer
Possible candidates are: Titanate Ceramics, Mica, Steatite, Soda–lime glass, Porcelain, and Phenol formaldehyde.
Work Step by Step
Given:
A parallel-plate capacitor with dimensions of 38 mm by 65 mm (1.5 in. by 2.5 in.) and a plate separation of 1.3 mm (0.05 in.) must have a minimum capacitance of 70 pF ($7 \times 10^{-11} F$) when an AC potential of 1000 V is applied at a frequency of 1 MHz
Required:
possible candidate materials from Table 18.5
Solution:
The minimum value of the dielectric constant must be computed. Using a combination of Equation 18.26 and 18.27:
$ε_{r} = \frac{ε}{ε_{0}} = \frac{lC}{ε_{0}A}$
$ε_{r} = \frac{(1.3 \times 10^{-3} m)(7 \times 10^{-11} F)}{(8.85 \times 10^{-12} F/m)(38 \times 10^{-3} m)(65 \times 10^{-3} m)} = 4.16 $
The minimum value of $ε_{r}$ to achieve the desired capacitance must be 4.16, and from Table 18.5, the materials with $ε_{r}$ higher than this value are: Titanate Ceramics, Mica, Steatite, Soda–lime glass, Porcelain, and Phenol formaldehyde.
