Physics 2102 Jonathan Dowling Physics 2102 Lecture 11 FRI 06 FEB Capacitance I 25 1 3 Tutoring Lab Now Open Tuesdays Lab Location 102 Nicholson across the hall from class Lab Hours MTWT 12 00N 5 00PM F 12 N 3 00PM Capacitors and Capacitance Capacitor any two conductors one with charge Q other with charge Q Potential DIFFERENCE between conductors V Q CV where C capacitance Units of capacitance Farad F Coulomb Volt Q Q Uses storing and releasing electric charge energy Most electronic capacitors micro Farads F pico Farads pF 10 12 F New technology compact 1 F capacitors Capacitance Capacitance depends only on GEOMETRICAL factors and on the MATERIAL that separates the two conductors e g Area of conductors separation whether the space in between is filled with air plastic etc Q Q We first focus on capacitors where gap is filled by AIR Electrolytic 1940 70 Electrolytic new Paper 1940 70 Capacitors Variable air mica Tantalum 1980 on Ceramic 1930 on Mica 1930 50 Parallel Plate Capacitor We want capacitance C Q V E field between the plates Gauss Law Q E 0 0 A Relate E to potential difference V Area of each plate A Separation d charge area Q A Q d Q Qd dx V E dx A 0 A 0 0 0 d What is the capacitance C Q 0 A C V d C 2 m2 C 2 CC C Units 2 Nm m Nm J V Q Capacitance and Your iPhone Q 0 A C V d Parallel Plate Capacitor Example A huge parallel plate capacitor consists of two square metal plates of side 50 cm separated by an air gap of 1 mm What is the capacitance C 0A d 8 85 x 10 12 F m 0 25 m2 0 001 m 2 21 x 10 9 F Very Small Lesson difficult to get large values of capacitance without special tricks C 2 m2 C 2 CC C Units F Farad 2 Nm m Nm J V Isolated Parallel Plate Capacitor A parallel plate capacitor of capacitance C is charged using a battery Charge Q potential difference V Battery is then disconnected If the plate separation is INCREASED does Potential Difference V a Increase b Remain the same c Decrease Q is fixed C decreases 0A d V Q C V increases Q Q Parallel Plate Capacitor Battery A parallel plate capacitor of capacitance C is charged using a battery Charge Q potential difference V Plate separation is INCREASED while battery remains connected Does the Electric Field Inside a Increase b Remain the Same V is fixed by battery c Decrease C decreases e0A d Q CV Q decreases E Q 0A decreases Q Q Spherical Capacitor What is the electric field inside the capacitor Gauss Law Q E 2 4 0 r Relate E to potential difference between the plates Radius of outer plate b Radius of inner plate a Concentric spherical shells Charge Q on inner shell Q on outer shell b b kQ kQ V E dr 2 dr r r a a a b 1 1 kQ a b Spherical Capacitor What is the capacitance C Q V Q Q 1 1 4 0 a b 4 0 ab b a Radius of outer plate b Radius of inner plate a Concentric spherical shells Charge Q on inner shell Q on outer shell Isolated sphere let b a C 4 0 a Cylindrical Capacitor What is the electric field in between the plates Gauss Law Radius of outer plate b Radius of inner plate a Q E 2 0 rL Length of capacitor L Q on inner rod Q on outer shell Relate E to potential difference between the plates V E dr b a b 2 0 L C Q V b ln a b b Q ln r Q Q ln dr rL 2 0 2 0 L a 2 0 L a a cylindrical Gaussian surface of radius r Summary Any two charged conductors form a capacitor Capacitance C Q V Simple Capacitors Parallel plates C 0 A d Spherical C 4 e0 ab b a Cylindrical C 2 0 L ln b a
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