Capacitors A system of two isolated conduct one separated by an insulator conductor is where charged with a charge Q with a charge and the other Q is called capacitor The sy bol used to indicate a capacitor two parallel lines is a At O g y 0 o D the capacitor a the absolute value Ue unter to the charge of of the charge on either plate The electric potential of the positive charge and of the negative charges conductor is Ut louder or We use the potential difference is V U for Ut K V an CV I p I a If we plot the change function of U gas this function is linear the relation and between potential difference ed chargeQ is follows as C V Tousled We call this constant the capacitance C The called the unit of the capacitance is Farad F EYE a capacitor changing Oun possibility to change a capacitor is the potential difference g to connect to a battery which suplies V f G tD I close the suith the two are If conductors of the capacitor connected to tha two poles of the battery The battery s positive terminal removes electrons from the raparilous conductor while the battery s negative terminal supplies electrons to the other conduitor of All charge movement stops when the potential difference between the conductor becomes equal to the potential difference between the battery terminals the capacitor calculating the capacitance Mfg the capanituce depends on the geometry of the plates and also on the material that e I separates the plates To calculate the capa it oil thy electric fieldE we can use conidualors Recipe I o d Assume we have the sa but opposite sign changes on both plates a 2 Use Gauss law to determine the electric field between the plates 3 Determine the potential differece U between the plates using d v V V is calculated along any fro thepositive The integral that takes us path to the negative plate The capacitance 4 by using I Spherical capacitor consists of two concentric shells with radii To calculate its capacitance we Ust can a cab Q o o f Ifiton t is U k what V In U V V V L I I V KE Qk I c Eta Ilia Tapproadmsiy V f Ed fleur af H H nifty C I IT y 41Ts lita Capacities of a parallelplate capacitor Gaussiansurface M ii ad are separated by a has a clang t g ed the right plate a charge g The electric flux is only areas where the flux of A E EA cos 0 will count to EA E E AE The potential difference U between the plates V U U EIds Ed III ds IT I Equivalent Capacitor There are for more circuit two possible configurations than in a capacitor one l parallel configuration bath To calculate thy total capacitance we can add the individual capacities G la C t Cz E Ci 2 serial configuration batter To calculate the total capacitance have to add up the inverse we capacitor for each capalito It t Energy stored in a capacitor the work U spent to charge a is stored in the for of capacitor potential Energy U W Wu can capacitor retrieve this energy is discharged U E CE when the Energy density where is The energy is between tha potential energy stored in the space the capacitorplates The electric field can store stored energy t u the volume of the field in a plate capacitor I V A d i is n i E E Capacitor with a dielectric Michael Faraday investigated the influence of inside a capacitor He discovered of dielectric material the capacitor increased is inserted that non if the capacitance a conductive materials the new capacitor is given by g g p K C C Ihappa Empty k the dielectric constant 2L 1 soca dielectrics we call for all materials Values for Material air Polystyrene Oil Glass strontia Titanate 22 1 000511 2 6 4 5 4 7 310 Two possible ways to increase the a capacitor with a capacitance dielectric of 1 Capacitor voltage remains constant bally dielectric The battery takes eave that the potential J difference stays the save P The new capacitance C Y KY Ken Capacitor charge g ve a ins tousled 2 M IT no capacity is thy with an open switch the charge slags rousted c I 24Cair Dielectric breakthrough is larger the Voltage applied to the If capacitor voltage of the dielectric conductivea spark or electric discharge happens that usually destroys the la pacilov than the breakthrough means it becomes