Physics Jonathan Dowling. Physics 2102 Lecture 7 Capacitors I

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1 Physics 2102 Jonathan Dowling Physics 2102 Lecture 7 Capacitors I

2 Capacitors and Capacitance Capacitor: any two conductors, one with charge +, other with charge Potential DIFFERENCE etween conductors = V = CV where C = capacitance Units of capacitance: Farad (F) = Coulom/Volt + Uses: storing and releasing electric charge/energy. Most electronic capacitors: micro-farads (µf), pico-farads (pf) F New technology: compact 1 F capacitors

3 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 etween is filled with air, plastic, etc. + (We first focus on capacitors where gap is filled y AIR!)

Electrolytic (1940-70) Electrolytic (new) Paper (1940-70) Capacitors

4 Electrolytic ( ) Electrolytic (new) Paper ( ) Capacitors Variale air, mica Tantalum (1980 on) Ceramic (1930 on) Mica (

5 Parallel Plate Capacitor E field etween the plates: (Gauss Law) V We want capacitance: C=/V Relate E to potential difference V: d r r =! E " dx 0 E = " =! 0! 0 A d = " dx =! A What is the capacitance C? d A 0 0! 0 V! A d 0 C = = + - Area of each plate = A Separation = d charge/area = σ = /A

6 Capacitance and Your ipod! V! A d 0 C = =

7 Parallel Plate Capacitor Example A huge parallel plate capacitor consists of two square metal plates of side 50 cm, separated y an air gap of 1 mm What is the capacitance? C = ε 0 A/d = (8.85 x F/m)(0.25 m 2 )/(0.001 m) = 2.21 x 10 9 F (Very Small!!) Lesson: difficult to get large values of capacitance without special tricks!

8 Isolated Parallel Plate Capacitor A parallel plate capacitor of capacitance C is charged using a attery. Charge =, potential difference = V. Battery is then disconnected. If the plate separation is INCREASED, does Potential Difference V: + (a) Increase? () Remain the same? (c) Decrease? is fixed! C decreases (=ε 0 A/d) =CV; V increases.

9 Parallel Plate Capacitor & Battery A parallel plate capacitor of capacitance C is charged using a attery. Charge =, potential difference = V. Plate separation is INCREASED while attery remains connected. + Does the Electric Field Inside: (a) Increase? () Remain the Same? (c) Decrease? V is fixed y attery! C decreases (=ε 0 A/d) =CV; decreases E = / ε 0 A decreases

10 Spherical Capacitor V What is the electric field inside the capacitor? (Gauss Law) E = 4!" r Relate E to potential difference etween the plates: r r =! E " dr a a 0 2 Radius of outer plate = Radius of inner plate = a Concentric spherical shells: Charge + on inner shell, on outer shell k & k# = dr = ' & 1 1# ( 2 r $% r!" = k ' $% a! " a

11 Spherical Capacitor What is the capacitance? C = /V = = () 4 0 & 1 $ % a 4 0 = "# (! ' a a) 1 #! " Radius of outer plate = Radius of inner plate = a Concentric spherical shells: Charge + on inner shell, on outer shell Isolated sphere: let >> a, C = 4!" a 0

12 Cylindrical Capacitor V What is the electric field in etween the plates? Gauss Law! E = 2!" 0 rl Relate E to potential difference etween the plates: r r =! E " dr a = ' a & ln dr = $ 2 () 0rL % 2() 0 r L #! " a Radius of outer plate = Radius of inner plate = a Length of capacitor = L + on inner rod, on outer shell = 2'( 0L & ln $ % a #! " cylindrical Gaussian surface of radius r

13 Summary Any two charged conductors form a capacitor. Capacitance : C= /V Simple Capacitors: Parallel plates: Spherical: Cylindrical: C = ε 0 A/d C = 4π ε 0 a/(-a) C = 2π ε 0 L/ln(/a)]

14 Capacitors in Parallel A wire is an equipotential surface! Capacitors in parallel have SAME potential difference ut NOT ALWAYS same charge! A 1 C 1 B V AB = V CD = V C 2 C 2 D total = C eq V = C 1 V + C 2 V C eq = C 1 + C 2 Equivalent parallel capacitance = sum of capacitances total C eq

15 Capacitors in Series 1 = 2 = (WHY??) V AC = V AB + V BC A Ceq = C + 1 C = + C eq C 1 1 C B C 1 C 2 C SERIES: is same for all capacitors Total potential difference = sum of V C eq

Physics Lecture: 16 MON 23 FEB Capacitance I

Physics Lecture: 16 MON 23 FEB Capacitance I Physics 2113 Jonathan Dowling Physics 2113 Lecture: 16 MON 23 FEB Capacitance I Capacitors and Capacitance Capacitor: any two conductors, one with charge +Q, other with charge Q Potential DIFFERENCE between