You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential

step 1 All right. So for this problem, we have a cylindric capacitor here, and the materials between th

You are asked to construct a capacitor having a capacitance...

You are asked to construct a capacitor having a capacitance near 1 $\mathrm{nF}$ and a breakdown potential in excess of 10$~ 000 \mathrm{V}$ . 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 $\mathrm{cm}$ tall with an inner radius of 3.6 $\mathrm{cm}$ and an outer radius of 3.8 $\mathrm{cm} .$ What are the (a) capacitance and (b) breakdown potential of this capacitor?

You are asked to construct a capacitor having a capacitance
near 1 $\mathrm{nF}$ and a breakdown potential in excess of 10$~ 000 \mathrm{V}$ . 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 $\mathrm{cm}$ tall with an inner radius of
3.6 $\mathrm{cm}$ and an outer radius of 3.8 $\mathrm{cm} .$ What are the (a) capacitance
and (b) breakdown potential of this capacitor?

Key Concepts

Dielectric Breakdown

Dielectric breakdown is the phenomenon where an insulating material becomes conductive when subjected to a voltage that exceeds its maximum withstand capacity. It defines the upper limit of the voltage that a capacitor can safely handle. The breakdown voltage is a critical specification and is determined by both the inherent breakdown strength of the dielectric material and the thickness of the dielectric layer.

Dielectric Materials

Dielectric materials are insulating substances placed between the plates of a capacitor to increase its capacitance by reducing the effective electric field. They are characterized by their dielectric constant (or relative permittivity) which enhances the capacitance compared to a vacuum. In practical designs, the choice of dielectric also influences other important properties such as the breakdown potential.

Capacitance

Capacitance is the measure of a capacitor's ability to store electric charge per unit potential difference. It depends on the geometry of the conductors and the properties of the material (dielectric) between them. In cylindrical capacitors, the capacitance is expressed using a formula that involves the permittivity of the dielectric, the length of the capacitor, and a logarithmic term reflecting the ratio of the radii.

Cylindrical Capacitor Geometry

This concept involves the configuration where the capacitor consists of two coaxial cylindrical surfaces, one acting as the inner electrode and the other as the outer electrode. The capacitance in such a setup is calculated based on the length of the cylinders and the logarithmic ratio of the outer to the inner radii. It forms the foundation of analyzing and designing capacitors with curved geometries.

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