Question 25.44: You are asked to construct a capacitor having a capacitance ......
You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10 000 V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15 cm tall with an inner radius of 3.6 cm and an outer radius of 3.8 cm. What are the (a) capacitance and (b) breakdown potential of this capacitor?
(a) We use Eq. 25-14:
C=2 \pi \varepsilon_0 \frac{L}{\ln (b / a)} (cylindrical capacitor). (25-14)
C=2 \pi \varepsilon_0 \kappa \frac{L}{\ln (b / a)}=\frac{(4.7)(0.15 \,m )}{2\left(8.99 \times 10^9 \frac{ N \cdot m ^2}{ C ^2}\right) \ln (3.8\, cm / 3.6 \,cm )}=0.73 \,nF .
(b) The breakdown potential is (14 kV/mm) (3.8 cm – 3.6 cm) = 28 kV.