Physics Lecture 4: Capacitance (HUE AI 2024-2025)

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abd...

Physics BAS-101 First Level Fall Semester 2024-2025 1 By Ass. Prof. Mohamed Abdelghany Dr. Nermin Ali Abdelhakim Dr. Enas lotfy Faculty of AI , Level 1, Physics, Lecture 4  2 Foundations of Electricity Faculty of AI , Level 1, Physics, Lecture 4 3 Capacitance The basic elements of any capacitor are two isolated conductors of any shape. 4 ❑ The corresponding figure shows a less general but more conventional arrangement, called a parallel-plate capacitor, consisting of two parallel conducting plates of area A separated by a distance d. ❑ When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: +q and -q. 5 Because the plates are conductors, they are equipotential surfaces and all points on a plate are at the same electric potential. Moreover, there is a potential difference between the two plates V. 6 ❑ The charge q and the potential difference V for a capacitor are proportional to each other; that is, q= CV ❑ The proportionality constant C is called the capacitance of the capacitor. ❑ Its value depends only on the geometry of the plates and not on their charge or potential difference.  7 The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them.  8 ❖ The greater the capacitance, the more charge is required. ❖ The SI unit of capacitance is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad= 1 F = 1 coloumb / volt = 1 C/V The farad is a very large unit. Submultiples of the farad, such as the microfarad (1 μF = 10-6 F) and the picofarad (1 pF = 10-12 F), are more convenient units in practice. 9 10 11 12 13 14  Capacitor with a Dielectric 15 A dielectric is a nonconducting material such as rubber, glass, or waxed paper.  16 We can perform the following experiment to illustrate the effect of a dielectric in a capacitor. Consider a parallel-plate capacitor that without a dielectric has a charge Q0 and a capacitance C0. The potential difference across the capacitor is ∆V0= Q0/C0 17 ✓ Notice that no battery is shown in the figure; also, we must assume no charge can flow through an ideal voltmeter. ✓ Hence, there is no path by which charge can flow and alter the charge on the capacitor. ✓ If a dielectric is now inserted between the plates as in Figure, the voltmeter indicates that the voltage between the plates decreases to a value ∆V. ∆V= ∆V0 /k Because ∆V < ∆V0, we see that k > 1. ✓ The dimensionless factor k is called the dielectric constant of the material. 18 19 ❑ That is, the capacitance increases by the factor k when the dielectric completely fills the region between the plates. ❑ Because C0= Є0A/d for a parallel-plate capacitor, we can express the capacitance of a parallel-plate capacitor filled with a dielectric as: ❑ It would appear that the capacitance could be made very large by inserting a dielectric between the plates and decreasing d.  Therefore, a dielectric provides the following 20 advantages: ✓ An increase in capacitance ✓ An increase in maximum operating voltage ✓ Possible mechanical support between the plates, which allows the plates to be close together without touching, thereby decreasing d and increasing C. 21 22