Introduction to Electromagnetism - 10

Capacitance The capacitance, C, of a CAPACITOR (a system consisting of 2 conductors), is defined as the ratio of the charge on EITHER conductor to the magnitude of the potential difference. CAPACITY OF EARTH Parallel Plate Capacitor Calculating the Capacitance See Chapter 20, pp. 658-660 Parallel plate The capacitance of a parallel plate capacitor is proportional to the area of its plates and inversely proportional to their separation. Some Uses of Capacitors Summary of Capacitance Formulas Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 10 February 13, 2007 Let us assume that 2 conductors have equal and opposite charge. The electric field lines are perpendicular to the conductors They start from the positive charges and end up on the negative charges. All flux lines leaving one conductor end up at the other conductor (because they have the same Q ) V V- The electric field between the 2 conductors is In one dimension What happens when we double the charge The potential energy of the 2 conductors will also double MAIN POINT is a constant of the system. is called the capacitance of the system Units farad Let us consider a spherical conductor of radius R and charge Q (1st conductor). Let us assume that the second conductor is a concentric hollow sphere of infinite radius (V 0) The potential of the first sphere is which is also the potential difference with infinity. The capacitance depends only on the radius of the sphere, i.e., it depends only on the geometrical properties of the conductor. MAJOR POINTS The capacitance is a property of a conductor that depends on the geometry. Symbol for Capacitance Cylindrical Capacitor It is useful to define a capacitance per unit length Spherical Capacitor Two concentric spherical shells, of radii a and b CHARGING A CAPACITOR Let us take a battery, which is a device that is able to keep a certain potential difference between its terminals (where the charge comes in and goes out). The switch S is open. H and L will have the same, opposite charge. Initially, V 0. When the potential across the capacitor will equal the potential across the battery, the charge flow will stop and the capacitor will be fully charged. CAPACITORS IN PARALLEL Two capacitors are in parallel when both left plates are connected to one terminal ( ) and both right plates are connected to the other terminal (-). Let us examine the dynamics of the charges Electrons will flow from the left plates to the positive terminal and from the negative terminal to the right plates. The flow will stop when the plates reach the same potential of the battery. The total charge is Q Q1 Q2. The 2 capacitor have the same potential V1 V2 V. If instead of 2 capacitors C1 and C2 in parallel we had one capacitor C C1 C2, we would have the same amount of charge stored. Ceq is the combination of several capacitors into a single capacitor able to store the same amount of charge. In general, for capacitors in parallel Connected capacitors are said to be in parallel when the potential difference that is applied across their combination results in the same potential difference across each capacitor. The equivalent capacitance Ceq is always bigger than any single capacitor in the combination. CAPACITORS IN SERIES Two capacitors are in series when the left plate of one capacitor is connected to one terminal ( ) and the right plate of the other capacitor is connected to the other terminal (-). After we close the circuit, electrons are transferred from the left plate of C1 to the right plate of C2 through the battery. However, as a negative charge is being built on the right plate of C2, a corresponding positive charge is being induced on the left plate of C2, while a negative charge is induced on the right plate of C1. The charge is the same, the potentials are different. In general Capacitors are said to be in series when the potential difference across the combination is the sum of the potential difference across each individual capacitor. Ceq of capacitors in series is always smaller than any single capacitance. Example Find the equivalent resistance of the combination of capacitors in fig (a) Parallel Series G