Capacitance

1. Capacitance Definition Parallel Plate Capacitors Cylindrical Capacitor Spherical Capacitor Capacitors in Series and Parallel Energy Stored in an Electric Field Capacitor with a Dielectric Dielectrics and Gauss’ Law pps by C Gliniewicz

2. A capacitor consists of two isolated conductors of any shape. When one considers a capacitor of two parallel plates which each have the same charge, the plates are equipotential surfaces. All points on the plates have the same electric potential and form an equipotential surface. Capacitance is measured in farads. One farad is equal to one coulomb per volt. A capacitor consisting of two parallel plates has a capacitance equal to A cylindrical capacitor consisting of an axial wire and an outer cylinder with equal and opposite charges on the facing interior surfaces has a capacitance of pps by C Gliniewicz

3. A spherical capacitor consists of two concentric spheres with equal charges on the facing surfaces. The capacitance of a spherical capacitor is An isolated sphere can have a capacitance. Using the formula for a spherical capacitor and letting b→∞. Letting R be the radius of the sphere, one finds In circuits, one can connect capacitors in series or in parallel to one another. In a parallel configuration, one can easily see that the potential difference across each capacitor is the same as the potential difference of the power source. pps by C Gliniewicz

4. The total charge, q, is the sum of the charges on all the capacitors. Capacitors in parallel can be replaced with an equivalent capacitor which has the same total charge, q, and the same potential difference. If one has three capacitors in parallel, When a potential difference is applied across several capacitors connected in series, the capacitors have identical charge, q. The sum of the potential differences across all the capacitors is equal applied potential difference. Capacitors that are connected in series can be replaced with an equivalent capacitor that has the same charge, q, and the same potential difference as the actual series capacitors. pps by C Gliniewicz

5. Work must be done by an external agent in order to charge a capacitor. The work done to move all the electrons from one plate to the other is equal to the potential energy stored in the capacitor. Energy density is the potential energy in the capacitor per unit volume of the capacitor. The volume is just the area multiplied by the spacing, d. Nearly all capacitors have some substance separating the two plates. Michael Faraday found that placing a substance between the plates increased the capacitance by a factor, κ (kappa) which he called the dielectric constant. The dielectric constant of a vacuum is one by definition. The dielectric material also has the effect to limit the electric potential which can be applied between the plates. If this ‘breakdown potential’ is exceeded, the dielectric becomes a conductor between the plates of the capacitor. pps by C Gliniewicz

6. If one knows the capacitance in air (which is nearly the same as a vacuum since air is mostly empty space), then the capacitance with a dielectric is κ multiplied by the original capacitance. The electric field on a particle inside the dielectric and the electric field outside the surface of the plate of the capacitor are both changed by adding the dielectric constant, κ, in front of the permittivity constant. Gauss’ Law can be used in the dielectric, but it also is modified by placing κ with the permittivity constant. pps by C Gliniewicz