Capacitors. C d. An electrical component which stores charge. parallel plate capacitor. Scale in cm

Transcription

1 apaciors An elecrical componen which sores charge E 2 2 d A 2 parallel plae capacior Scale in cm

2 Leyden Jars I was invened independenly by German cleric Ewald Georg von Kleis on Ocober 745 and by Duch scienis Pieer van Musschenbroek of Leiden (Leyden) in

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4 Parallel plae capacior

5 A dielecric increases he charge on he plaes d A

6 apaciance is measured in Farads -2 pf = F F means one coulomb per uni vol beween he capacior plaes. A Leyden Jar has a capaciance of around nf. A ypical circui board capacior will have capaciance from a few pf up o a large number of mf apaciors in a parallel configuraion each have he same applied volage. The oal charge sored is herefore 2... n Since he oal capaciance is given by /... 2 n Therefore parallel capaciances add

7 Sum of volage drops across capaciors mus equae o he applied volage 2... n n Hence: n n n n n Now he charge on each adjacen capacior plae mus be he same, oherwise curren would flow beween he capaciors, re-apporioning charge 2... n Hence:... 2 n Therefore he reciprocals of series capaciances add

8 apaciance examples 2 3?? ?? ? 2 2? 3 2

9 Energy sored in a capacior The insananeous power required o esablish volage across he plaes of a capacior is P I In ime inerval d, he amoun of charge added o he capacior is d d Hence curren I is P P I d d Toal energy required o esablish volage across he capacior plaes (in ime ) is herefore d E Pd d d 2 E d E 2 I d d d d E 2 2

10 The capaciance of a meal sphere of radius R is given by 4 R The permiiviy of free space is 8.85 Fm 2 - So he apaciance of a.2m radius an der Graaf generaor is abou 22pF The energy sored in a capacior is E 2 2 The volage of a ypical an der Graaf migh be as high as 3k Hence he energy discharged is only abou J and he charge abou 6.6m 2 Reference

11 apaciors, combined wih oher basic componens such as resisors and inducors can form a huge variey of circuis, each wih a differen applicaion. An inegraed circui (on a chip ) is he basis of modern elecronics. A compuer microprocessor may conain billions of circuis! This paricular circui generaes a sine wave oscillaing signal a a frequency dependen upon he parameers of he componens i.e. capaciance, inducance ec

12 harging a capacior using a D source. Swich closed. urren flows hrough resisor and posiive charge builds up on righ capacior plae. An equal amoun of negaive charge builds up on lef plae. 2. Elecrical field se up beween capacior plaes as no curren can flow. olage beween he plaes is = / where is he oal charge deposied and is he capaciance ( charge per uni vol ) Swich R 3. As charge builds up on righ plae, poenial difference beween capacior and source reduces. This reduces he curren flowing ono he plae. Evenually he volage becomes and hence no more curren can flow. 3. Noe he amoun of charge which can be deposied depends on he resuling elecrical field srengh beween he plaes. Above he breakdown field srengh, curren will flow beween he plaes Dielecric Air 3 x 6 Mineral oil 5 x 6 Neoprene 6 x 6 Waer 65 x 6 Breakdown field srengh /m - Mica 8 x 6

13 harging a capacior using a D source IR I capacior charge, volage relaionship Ohm s law d d Definiion of curren d I R d d d d R R ln ln ln R e R ln R e R R

14 Discharging a capacior d IR I d capacior charge, volage relaionship I R d d Ohm s law Noe = when = Definiion of curren, and negaive since charge is discharged from plaes R R R ln ln d e R d R e R So R is a characerisic ime for charging or discharging a capacior R