184_notes:cap_in_cir

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184_notes:cap_in_cir [2021/03/12 17:34] – bartonmo184_notes:cap_in_cir [2021/06/15 00:35] (current) – schram45
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 **Capacitance** is defined as the proportionality constant of the potential difference between the plates of the capacitor ($| \Delta V| $) and the amount of charge that is on one plate ($|Q|$) - if the charge increases, the potential difference should increase and vice versa. Note that since one plate will always have a charge of +Q and one will have a charge of -Q (because of conservation of charge), the $|Q|$ will be the same no matter which plate you are looking at. In terms of an equation, this means that: **Capacitance** is defined as the proportionality constant of the potential difference between the plates of the capacitor ($| \Delta V| $) and the amount of charge that is on one plate ($|Q|$) - if the charge increases, the potential difference should increase and vice versa. Note that since one plate will always have a charge of +Q and one will have a charge of -Q (because of conservation of charge), the $|Q|$ will be the same no matter which plate you are looking at. In terms of an equation, this means that:
 $$|Q|=C|\Delta V|$$ $$|Q|=C|\Delta V|$$
-The units of capacitance are then **coulombs/volt (C/V), which is called a farad** (named after [[https://en.wikipedia.org/wiki/Michael_Faraday|Michael Faraday]]) and abbreviated with "F". A 1 F capacitor is an extremely large capacitor - large in physical size and also takes a long time to charge/discharge. A typical capacitor in electronic capacitors is on the order of nanofarads ($10^{-9}$) to picofarads ($10^{-12}$).+The units of capacitance are then **coulombs/volt (C/V), which is called a farad** (named after [[https://en.wikipedia.org/wiki/Michael_Faraday|Michael Faraday]]) and abbreviated with "F". A 1 F capacitor is an extremely large capacitor - large in both in physical size and the amount of time it takes to charge/discharge. A typical capacitor in electronic capacitors is on the order of nanofarads ($10^{-9}$) to picofarads ($10^{-12}$).
  
 ==== Finding Capacitance ==== ==== Finding Capacitance ====
 We can actually find an expression for capacitance specifically for parallel plates using the [[184_notes:pc_vefu|relationship between electric field and electric potential]] and the definition of capacitance above. //__Assume we start with a pair of parallel plates__//, which have an area $A$, a charge of $+/-Q$, and are separated by a distance $d$. We can actually find an expression for capacitance specifically for parallel plates using the [[184_notes:pc_vefu|relationship between electric field and electric potential]] and the definition of capacitance above. //__Assume we start with a pair of parallel plates__//, which have an area $A$, a charge of $+/-Q$, and are separated by a distance $d$.
  
-[{{ :184_notes:e-field_between_parallel_plates_new.png?350|Electric field between two parallel plates. The dashed blue arrows represent the E-field from the negatively charged plate, and the solid red arrows represent the positive plate. }}]+[{{ :184_notes:e-field_between_parallel_plates_new.png?300|Electric field between two parallel plates. The dashed blue arrows represent the E-field from the negatively charged plate, and the solid red arrows represent the positive plate. }}]
  
 ==== Deriving the Capacitance for Parallel Plates ==== ==== Deriving the Capacitance for Parallel Plates ====
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 ==== Examples ==== ==== Examples ====
-[[:184_notes:examples:Week7_energy_plate_capacitor|Energy Stored in a Parallel Plate Capacitor]] +  * [[:184_notes:examples:Week7_energy_plate_capacitor|Energy Stored in a Parallel Plate Capacitor]] 
- +    * Video Example: Energy Stored in a Parallel Plate Capacitor 
-[[:184_notes:examples:Week7_cylindrical_capacitor|Finding the Capacitance of a Cylindrical Capacitor]]+  * [[:184_notes:examples:Week7_cylindrical_capacitor|Finding the Capacitance of a Cylindrical Capacitor]] 
 +    * Video Example: Finding the Capacitance of a Cylindrical Capacitor 
 +{{youtube>AAGXqz2JMbc?large}} 
 +{{youtube>vp_VWtwdMkE?large}}
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  • Last modified: 2021/03/12 17:34
  • by bartonmo