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25-2. Capacitance charge storage, energy storage Given As a Result Capacitor:  Any two isolated conductors
25-2. Capacitance Units of capacitance:  Farad  (F) = Coulomb/Volt Potential (or Voltage) Capacitance
25-2. Capacitance +q -q E field between the plates: (Gauss’ Law) Relate  E  to potential difference  V : What is the capacitance  C  ? Area of each plate  = A Separation  = d charge/area  =   = q/A
25-2. Capacitance Capacitance  and Your iPod
25-2. Capacitance ,[object Object],[object Object],C =    0  A/d  = (8.85 x 10 –12  F/m)(0.25 m 2 )/(0.001 m) = 2.21 x 10 –9  F ( Very Small!! ) Units of capacitance:  Farad  (F) = Coulomb/Volt
25-2. Capacitance ,[object Object],[object Object],[object Object],Determine what is NOT changed.
25-2. Capacitance ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Does the  Electric Field  Inside: (a) Increase? (b) Remain the Same? (c) Decrease? +Q – Q
25-3. Calculating the Capacitance Cylindrical Capacitor
25-3. Calculating the Capacitance Spherical Capacitor
25-3. Calculating the Capacitance Capacitance of a single conducting sphere Spherical Capacitor
25-4. C in Parallel and in Series  Q:  the same V:  the same Parallel Series
25-4. C in Parallel and in Series  ,[object Object],[object Object],[object Object],[object Object],[object Object],V:  the same Parallel A B C D C 1 C 2 Q 1 Q 2 C eq Q total
25-4. C in Parallel and in Series  ,[object Object],[object Object],Q:  the same Series A B C C 1 C 2 Q 1 Q 2 C eq Q
25-4. Example 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],10   F 30   F 20   F 120V What is the charge on each capacitor?
25-4. Example 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],10   F 30   F 20   F 120V What is the potential difference across each capacitor?
25-4. Example 3 ,[object Object],[object Object],[object Object],What is the charge on the 10  F capacitor? 10   F 5   F 5   F 10V 10   F 10   F 10V
25-4. Example 4 (N-1) Capacitors with A and d:  Parallel Connection + –
25-4. Example 5 ,[object Object],[object Object],[object Object],Initial charge on 10  F = (10  F)(120V)= 1200  C After switch is closed, let charges = Q 1  and Q 2 .  Charge is conserved: Q 1  + Q 2  = 1200  C And, V final  is same:  ,[object Object],[object Object],[object Object],What is the charge on each capacitor? 10  F (C 1 ) 20  F (C 2 )
 
25-5. Energy Stored ,[object Object],[object Object],[object Object],dq
25-5. Energy Stored in an E-Field ,[object Object],[object Object],[object Object],[object Object],General expression for any region with vacuum (or air)
25-6. Capacitor with a Dielectric Dielectric: Noncoducting material HW5-8 Breakdown Potential:  Dielectric Strength (kV/mm) X Length (mm)
25-6. Capacitor with a Dielectric or ??
25-6. Capacitor with a Dielectric
25-6. Capacitor with a Dielectric
25-6. Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],dielectric  slab
25-6. Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],dielectric  slab
 

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Capacitance