Intuition for capacitors in seriesCapacitors in series?Capacitors in series: Why is the equivalent charge the same as the individual chargesCapacitors in a series circuit with dielectricCircuit with three capacitorsVoltage drop across capacitors in series, why?Relyance of plate distance on the capacitor equationUnsure of capacitor in series & in parallelEquivalent capacitance in seriesCapacitors in Series, which uses the most voltage?Infinite ladder of capacitors

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Intuition for capacitors in series


Capacitors in series?Capacitors in series: Why is the equivalent charge the same as the individual chargesCapacitors in a series circuit with dielectricCircuit with three capacitorsVoltage drop across capacitors in series, why?Relyance of plate distance on the capacitor equationUnsure of capacitor in series & in parallelEquivalent capacitance in seriesCapacitors in Series, which uses the most voltage?Infinite ladder of capacitors






.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;








3












$begingroup$


Can someone please explain, intuitively (without any formula, I understand the formulas), why the equivalent capacitance of capacitors in series is less than the any individual capacitor's capacitance?



PS: Let's take a simple case. Say we have 2 capacitors with Capacitance 2 (ignoring units), and we place them in series. A voltage $V$ develops in both, and a charge $+Q$ acculumates on one of their plates. Using the capacitance formulas, the equivalent capacitance is $1/2$ the original. Indeed we get $Q/2V$, where $Q/V$ is the original capacitance. But why? aren't we in total acculumating a charge of $2Q$ over a potential difference of $2V$? Why just $1Q$? (again, I'm speaking intuitively)










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$endgroup$











  • $begingroup$
    Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
    $endgroup$
    – PM 2Ring
    8 hours ago










  • $begingroup$
    Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
    $endgroup$
    – user10796158
    8 hours ago










  • $begingroup$
    Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
    $endgroup$
    – BillDOe
    8 hours ago






  • 1




    $begingroup$
    Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
    $endgroup$
    – PM 2Ring
    8 hours ago






  • 1




    $begingroup$
    @PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
    $endgroup$
    – user10796158
    8 hours ago

















3












$begingroup$


Can someone please explain, intuitively (without any formula, I understand the formulas), why the equivalent capacitance of capacitors in series is less than the any individual capacitor's capacitance?



PS: Let's take a simple case. Say we have 2 capacitors with Capacitance 2 (ignoring units), and we place them in series. A voltage $V$ develops in both, and a charge $+Q$ acculumates on one of their plates. Using the capacitance formulas, the equivalent capacitance is $1/2$ the original. Indeed we get $Q/2V$, where $Q/V$ is the original capacitance. But why? aren't we in total acculumating a charge of $2Q$ over a potential difference of $2V$? Why just $1Q$? (again, I'm speaking intuitively)










share|cite|improve this question











$endgroup$











  • $begingroup$
    Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
    $endgroup$
    – PM 2Ring
    8 hours ago










  • $begingroup$
    Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
    $endgroup$
    – user10796158
    8 hours ago










  • $begingroup$
    Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
    $endgroup$
    – BillDOe
    8 hours ago






  • 1




    $begingroup$
    Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
    $endgroup$
    – PM 2Ring
    8 hours ago






  • 1




    $begingroup$
    @PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
    $endgroup$
    – user10796158
    8 hours ago













3












3








3





$begingroup$


Can someone please explain, intuitively (without any formula, I understand the formulas), why the equivalent capacitance of capacitors in series is less than the any individual capacitor's capacitance?



PS: Let's take a simple case. Say we have 2 capacitors with Capacitance 2 (ignoring units), and we place them in series. A voltage $V$ develops in both, and a charge $+Q$ acculumates on one of their plates. Using the capacitance formulas, the equivalent capacitance is $1/2$ the original. Indeed we get $Q/2V$, where $Q/V$ is the original capacitance. But why? aren't we in total acculumating a charge of $2Q$ over a potential difference of $2V$? Why just $1Q$? (again, I'm speaking intuitively)










share|cite|improve this question











$endgroup$




Can someone please explain, intuitively (without any formula, I understand the formulas), why the equivalent capacitance of capacitors in series is less than the any individual capacitor's capacitance?



PS: Let's take a simple case. Say we have 2 capacitors with Capacitance 2 (ignoring units), and we place them in series. A voltage $V$ develops in both, and a charge $+Q$ acculumates on one of their plates. Using the capacitance formulas, the equivalent capacitance is $1/2$ the original. Indeed we get $Q/2V$, where $Q/V$ is the original capacitance. But why? aren't we in total acculumating a charge of $2Q$ over a potential difference of $2V$? Why just $1Q$? (again, I'm speaking intuitively)







capacitance






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 35 mins ago









Emilio Pisanty

88.7k23 gold badges225 silver badges458 bronze badges




88.7k23 gold badges225 silver badges458 bronze badges










asked 9 hours ago









user10796158user10796158

274 bronze badges




274 bronze badges











  • $begingroup$
    Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
    $endgroup$
    – PM 2Ring
    8 hours ago










  • $begingroup$
    Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
    $endgroup$
    – user10796158
    8 hours ago










  • $begingroup$
    Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
    $endgroup$
    – BillDOe
    8 hours ago






  • 1




    $begingroup$
    Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
    $endgroup$
    – PM 2Ring
    8 hours ago






  • 1




    $begingroup$
    @PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
    $endgroup$
    – user10796158
    8 hours ago
















  • $begingroup$
    Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
    $endgroup$
    – PM 2Ring
    8 hours ago










  • $begingroup$
    Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
    $endgroup$
    – user10796158
    8 hours ago










  • $begingroup$
    Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
    $endgroup$
    – BillDOe
    8 hours ago






  • 1




    $begingroup$
    Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
    $endgroup$
    – PM 2Ring
    8 hours ago






  • 1




    $begingroup$
    @PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
    $endgroup$
    – user10796158
    8 hours ago















$begingroup$
Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
$endgroup$
– PM 2Ring
8 hours ago




$begingroup$
Is it intuitive for you that for capacitors in parallel, the equivalent capacitance is equal to the sum of all the capacitors?
$endgroup$
– PM 2Ring
8 hours ago












$begingroup$
Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
$endgroup$
– user10796158
8 hours ago




$begingroup$
Actually, I haven't thought about that case yet, because the book I'm using presents the series equations first. Are you suggesting that understanding the parallel case sheds light on this case?
$endgroup$
– user10796158
8 hours ago












$begingroup$
Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
$endgroup$
– BillDOe
8 hours ago




$begingroup$
Well, for one thing the first capacitor has to charge and then discharge before the second capacitor can charge.
$endgroup$
– BillDOe
8 hours ago




1




1




$begingroup$
Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
$endgroup$
– PM 2Ring
8 hours ago




$begingroup$
Not necessarily, but I think the parallel case is easier to understand than the series case, so to me it makes sense to consider it first.
$endgroup$
– PM 2Ring
8 hours ago




1




1




$begingroup$
@PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
$endgroup$
– user10796158
8 hours ago




$begingroup$
@PM2Ring you're right, I just read that section, and it actually makes sense why you would add the capacitances. In a way, it's like you're increasing the area by adding in parallel for the same voltage drop. But the series case still doesn't quite make sense to me.
$endgroup$
– user10796158
8 hours ago










3 Answers
3






active

oldest

votes


















8












$begingroup$


Can someone please explain, intuitively (without any formula, I
understand the formulas), why the equivalent capacitance of capacitors
in series is less than the any individual capacitor's capacitance?




I assume you know that the larger the capacitor plates are, the greater the capacitance, all other things being equal. Also I assume you know the greater the separation of the plates (the thicker the dielectric between the plates) the less the capacitance all other things being equal. Given these assumptions, consider the diagrams below.



The top diagram to the left shows two capacitors in parallel. It is equivalent to the digram to the top right. If two or more capacitors are connected in parallel, the overall effect is that of a single (equivalent) capacitor having a total plate area equal to the sum of the plate areas of the individual capacitors. Thus for parallel capacitors the equivalent capacitance is the sum of the capacitances.



The bottom diagram to the left shows two capacitors in series. It is equivalent to the diagram to the bottom right. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. Thus for series capacitors the equivalent capacitor is less than the individual capacitors.



For reference the diagram includes an equation for capacitance based on the physical parameters of plate area $A$, plate separation $d$, and electrical permittivity $e$ of the dielectric.



Hope this helps.



enter image description here






share|cite|improve this answer











$endgroup$












  • $begingroup$
    Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
    $endgroup$
    – user10796158
    7 hours ago










  • $begingroup$
    Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
    $endgroup$
    – user10796158
    7 hours ago










  • $begingroup$
    @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
    $endgroup$
    – Bob D
    7 hours ago


















2












$begingroup$

The voltage change across a capacitor, or any region of space, is the negative path integral of field dot path. So if two capacitors are placed in series, you have twice the distance for the path integral, compared to one capacitor by itself. Now, since the distance is doubled, to get a final voltage equal to the battery that charges it, the electric field only needs to be 1/2 the electric field of the single capacitor. Since the electric field is proportional to the charge density, you only need 1/2 the charge density that would be on the single capacitor, so C = (Qsingle/2)/V.






share|cite|improve this answer









$endgroup$




















    1












    $begingroup$


    why the equivalent capacitance of capacitors in series is less than
    the any individual capacitor's capacitance?




    To help build your intuition, place in series with another capacitor an ideal parallel plate capacitor (vacuum dielectric for simplicity), with plate spacing $d$. Now consider the limit as the distance $d$ goes to zero (assume zero initial charge).



    Intuitively, the capacitance of the ideal parallel plate capacitor increases without bound and what's left in the limit is, effectively, an ideal short circuit when $d = 0$ (the two plates touch).



    That is, the series combination of two capacitors has become a capacitor in series with an ideal short circuit. Clearly, the combined capacitance is just the capacitance of the remaining capacitor.



    Now, hold the spacing $d$ constant and let the plate area $A$ go to zero instead. Intuitively, the capacitance of the ideal plate capacitor goes to zero and what's left in the limit is, effectively, an ideal open circuit.



    That is, the series combination of two capacitors has become a capacitor in series with an ideal open circuit. Clearly, the combined capacitance is zero.



    It follows that the total capacitance for two series capacitors with finite capacitance is less than the smaller of the two capacitances






    share|cite|improve this answer









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      3 Answers
      3






      active

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      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      8












      $begingroup$


      Can someone please explain, intuitively (without any formula, I
      understand the formulas), why the equivalent capacitance of capacitors
      in series is less than the any individual capacitor's capacitance?




      I assume you know that the larger the capacitor plates are, the greater the capacitance, all other things being equal. Also I assume you know the greater the separation of the plates (the thicker the dielectric between the plates) the less the capacitance all other things being equal. Given these assumptions, consider the diagrams below.



      The top diagram to the left shows two capacitors in parallel. It is equivalent to the digram to the top right. If two or more capacitors are connected in parallel, the overall effect is that of a single (equivalent) capacitor having a total plate area equal to the sum of the plate areas of the individual capacitors. Thus for parallel capacitors the equivalent capacitance is the sum of the capacitances.



      The bottom diagram to the left shows two capacitors in series. It is equivalent to the diagram to the bottom right. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. Thus for series capacitors the equivalent capacitor is less than the individual capacitors.



      For reference the diagram includes an equation for capacitance based on the physical parameters of plate area $A$, plate separation $d$, and electrical permittivity $e$ of the dielectric.



      Hope this helps.



      enter image description here






      share|cite|improve this answer











      $endgroup$












      • $begingroup$
        Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
        $endgroup$
        – Bob D
        7 hours ago















      8












      $begingroup$


      Can someone please explain, intuitively (without any formula, I
      understand the formulas), why the equivalent capacitance of capacitors
      in series is less than the any individual capacitor's capacitance?




      I assume you know that the larger the capacitor plates are, the greater the capacitance, all other things being equal. Also I assume you know the greater the separation of the plates (the thicker the dielectric between the plates) the less the capacitance all other things being equal. Given these assumptions, consider the diagrams below.



      The top diagram to the left shows two capacitors in parallel. It is equivalent to the digram to the top right. If two or more capacitors are connected in parallel, the overall effect is that of a single (equivalent) capacitor having a total plate area equal to the sum of the plate areas of the individual capacitors. Thus for parallel capacitors the equivalent capacitance is the sum of the capacitances.



      The bottom diagram to the left shows two capacitors in series. It is equivalent to the diagram to the bottom right. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. Thus for series capacitors the equivalent capacitor is less than the individual capacitors.



      For reference the diagram includes an equation for capacitance based on the physical parameters of plate area $A$, plate separation $d$, and electrical permittivity $e$ of the dielectric.



      Hope this helps.



      enter image description here






      share|cite|improve this answer











      $endgroup$












      • $begingroup$
        Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
        $endgroup$
        – Bob D
        7 hours ago













      8












      8








      8





      $begingroup$


      Can someone please explain, intuitively (without any formula, I
      understand the formulas), why the equivalent capacitance of capacitors
      in series is less than the any individual capacitor's capacitance?




      I assume you know that the larger the capacitor plates are, the greater the capacitance, all other things being equal. Also I assume you know the greater the separation of the plates (the thicker the dielectric between the plates) the less the capacitance all other things being equal. Given these assumptions, consider the diagrams below.



      The top diagram to the left shows two capacitors in parallel. It is equivalent to the digram to the top right. If two or more capacitors are connected in parallel, the overall effect is that of a single (equivalent) capacitor having a total plate area equal to the sum of the plate areas of the individual capacitors. Thus for parallel capacitors the equivalent capacitance is the sum of the capacitances.



      The bottom diagram to the left shows two capacitors in series. It is equivalent to the diagram to the bottom right. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. Thus for series capacitors the equivalent capacitor is less than the individual capacitors.



      For reference the diagram includes an equation for capacitance based on the physical parameters of plate area $A$, plate separation $d$, and electrical permittivity $e$ of the dielectric.



      Hope this helps.



      enter image description here






      share|cite|improve this answer











      $endgroup$




      Can someone please explain, intuitively (without any formula, I
      understand the formulas), why the equivalent capacitance of capacitors
      in series is less than the any individual capacitor's capacitance?




      I assume you know that the larger the capacitor plates are, the greater the capacitance, all other things being equal. Also I assume you know the greater the separation of the plates (the thicker the dielectric between the plates) the less the capacitance all other things being equal. Given these assumptions, consider the diagrams below.



      The top diagram to the left shows two capacitors in parallel. It is equivalent to the digram to the top right. If two or more capacitors are connected in parallel, the overall effect is that of a single (equivalent) capacitor having a total plate area equal to the sum of the plate areas of the individual capacitors. Thus for parallel capacitors the equivalent capacitance is the sum of the capacitances.



      The bottom diagram to the left shows two capacitors in series. It is equivalent to the diagram to the bottom right. If two or more capacitors are connected in series, the overall effect is that of a single (equivalent) capacitor having the sum total of the plate spacings of the individual capacitors. Thus for series capacitors the equivalent capacitor is less than the individual capacitors.



      For reference the diagram includes an equation for capacitance based on the physical parameters of plate area $A$, plate separation $d$, and electrical permittivity $e$ of the dielectric.



      Hope this helps.



      enter image description here







      share|cite|improve this answer














      share|cite|improve this answer



      share|cite|improve this answer








      edited 7 hours ago

























      answered 8 hours ago









      Bob DBob D

      8,7603 gold badges7 silver badges29 bronze badges




      8,7603 gold badges7 silver badges29 bronze badges











      • $begingroup$
        Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
        $endgroup$
        – Bob D
        7 hours ago
















      • $begingroup$
        Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
        $endgroup$
        – user10796158
        7 hours ago










      • $begingroup$
        @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
        $endgroup$
        – Bob D
        7 hours ago















      $begingroup$
      Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
      $endgroup$
      – user10796158
      7 hours ago




      $begingroup$
      Bob, thank you for your answer. This is starting to make sense. But do you mind elaborating a teeny bit more on why the total charge for the series case is Q not 2Q?
      $endgroup$
      – user10796158
      7 hours ago












      $begingroup$
      Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
      $endgroup$
      – user10796158
      7 hours ago




      $begingroup$
      Because it seems to me that the overall effect of having two plates in series each with charge Q would give 2Q
      $endgroup$
      – user10796158
      7 hours ago












      $begingroup$
      @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
      $endgroup$
      – Bob D
      7 hours ago




      $begingroup$
      @user10796158 Ok but I need some time to respond because I need to tend to something else at this time. Please stand by.
      $endgroup$
      – Bob D
      7 hours ago













      2












      $begingroup$

      The voltage change across a capacitor, or any region of space, is the negative path integral of field dot path. So if two capacitors are placed in series, you have twice the distance for the path integral, compared to one capacitor by itself. Now, since the distance is doubled, to get a final voltage equal to the battery that charges it, the electric field only needs to be 1/2 the electric field of the single capacitor. Since the electric field is proportional to the charge density, you only need 1/2 the charge density that would be on the single capacitor, so C = (Qsingle/2)/V.






      share|cite|improve this answer









      $endgroup$

















        2












        $begingroup$

        The voltage change across a capacitor, or any region of space, is the negative path integral of field dot path. So if two capacitors are placed in series, you have twice the distance for the path integral, compared to one capacitor by itself. Now, since the distance is doubled, to get a final voltage equal to the battery that charges it, the electric field only needs to be 1/2 the electric field of the single capacitor. Since the electric field is proportional to the charge density, you only need 1/2 the charge density that would be on the single capacitor, so C = (Qsingle/2)/V.






        share|cite|improve this answer









        $endgroup$















          2












          2








          2





          $begingroup$

          The voltage change across a capacitor, or any region of space, is the negative path integral of field dot path. So if two capacitors are placed in series, you have twice the distance for the path integral, compared to one capacitor by itself. Now, since the distance is doubled, to get a final voltage equal to the battery that charges it, the electric field only needs to be 1/2 the electric field of the single capacitor. Since the electric field is proportional to the charge density, you only need 1/2 the charge density that would be on the single capacitor, so C = (Qsingle/2)/V.






          share|cite|improve this answer









          $endgroup$



          The voltage change across a capacitor, or any region of space, is the negative path integral of field dot path. So if two capacitors are placed in series, you have twice the distance for the path integral, compared to one capacitor by itself. Now, since the distance is doubled, to get a final voltage equal to the battery that charges it, the electric field only needs to be 1/2 the electric field of the single capacitor. Since the electric field is proportional to the charge density, you only need 1/2 the charge density that would be on the single capacitor, so C = (Qsingle/2)/V.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 6 hours ago









          lamplamplamplamp

          5541 gold badge5 silver badges19 bronze badges




          5541 gold badge5 silver badges19 bronze badges





















              1












              $begingroup$


              why the equivalent capacitance of capacitors in series is less than
              the any individual capacitor's capacitance?




              To help build your intuition, place in series with another capacitor an ideal parallel plate capacitor (vacuum dielectric for simplicity), with plate spacing $d$. Now consider the limit as the distance $d$ goes to zero (assume zero initial charge).



              Intuitively, the capacitance of the ideal parallel plate capacitor increases without bound and what's left in the limit is, effectively, an ideal short circuit when $d = 0$ (the two plates touch).



              That is, the series combination of two capacitors has become a capacitor in series with an ideal short circuit. Clearly, the combined capacitance is just the capacitance of the remaining capacitor.



              Now, hold the spacing $d$ constant and let the plate area $A$ go to zero instead. Intuitively, the capacitance of the ideal plate capacitor goes to zero and what's left in the limit is, effectively, an ideal open circuit.



              That is, the series combination of two capacitors has become a capacitor in series with an ideal open circuit. Clearly, the combined capacitance is zero.



              It follows that the total capacitance for two series capacitors with finite capacitance is less than the smaller of the two capacitances






              share|cite|improve this answer









              $endgroup$

















                1












                $begingroup$


                why the equivalent capacitance of capacitors in series is less than
                the any individual capacitor's capacitance?




                To help build your intuition, place in series with another capacitor an ideal parallel plate capacitor (vacuum dielectric for simplicity), with plate spacing $d$. Now consider the limit as the distance $d$ goes to zero (assume zero initial charge).



                Intuitively, the capacitance of the ideal parallel plate capacitor increases without bound and what's left in the limit is, effectively, an ideal short circuit when $d = 0$ (the two plates touch).



                That is, the series combination of two capacitors has become a capacitor in series with an ideal short circuit. Clearly, the combined capacitance is just the capacitance of the remaining capacitor.



                Now, hold the spacing $d$ constant and let the plate area $A$ go to zero instead. Intuitively, the capacitance of the ideal plate capacitor goes to zero and what's left in the limit is, effectively, an ideal open circuit.



                That is, the series combination of two capacitors has become a capacitor in series with an ideal open circuit. Clearly, the combined capacitance is zero.



                It follows that the total capacitance for two series capacitors with finite capacitance is less than the smaller of the two capacitances






                share|cite|improve this answer









                $endgroup$















                  1












                  1








                  1





                  $begingroup$


                  why the equivalent capacitance of capacitors in series is less than
                  the any individual capacitor's capacitance?




                  To help build your intuition, place in series with another capacitor an ideal parallel plate capacitor (vacuum dielectric for simplicity), with plate spacing $d$. Now consider the limit as the distance $d$ goes to zero (assume zero initial charge).



                  Intuitively, the capacitance of the ideal parallel plate capacitor increases without bound and what's left in the limit is, effectively, an ideal short circuit when $d = 0$ (the two plates touch).



                  That is, the series combination of two capacitors has become a capacitor in series with an ideal short circuit. Clearly, the combined capacitance is just the capacitance of the remaining capacitor.



                  Now, hold the spacing $d$ constant and let the plate area $A$ go to zero instead. Intuitively, the capacitance of the ideal plate capacitor goes to zero and what's left in the limit is, effectively, an ideal open circuit.



                  That is, the series combination of two capacitors has become a capacitor in series with an ideal open circuit. Clearly, the combined capacitance is zero.



                  It follows that the total capacitance for two series capacitors with finite capacitance is less than the smaller of the two capacitances






                  share|cite|improve this answer









                  $endgroup$




                  why the equivalent capacitance of capacitors in series is less than
                  the any individual capacitor's capacitance?




                  To help build your intuition, place in series with another capacitor an ideal parallel plate capacitor (vacuum dielectric for simplicity), with plate spacing $d$. Now consider the limit as the distance $d$ goes to zero (assume zero initial charge).



                  Intuitively, the capacitance of the ideal parallel plate capacitor increases without bound and what's left in the limit is, effectively, an ideal short circuit when $d = 0$ (the two plates touch).



                  That is, the series combination of two capacitors has become a capacitor in series with an ideal short circuit. Clearly, the combined capacitance is just the capacitance of the remaining capacitor.



                  Now, hold the spacing $d$ constant and let the plate area $A$ go to zero instead. Intuitively, the capacitance of the ideal plate capacitor goes to zero and what's left in the limit is, effectively, an ideal open circuit.



                  That is, the series combination of two capacitors has become a capacitor in series with an ideal open circuit. Clearly, the combined capacitance is zero.



                  It follows that the total capacitance for two series capacitors with finite capacitance is less than the smaller of the two capacitances







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 1 hour ago









                  Alfred CentauriAlfred Centauri

                  49.4k3 gold badges51 silver badges155 bronze badges




                  49.4k3 gold badges51 silver badges155 bronze badges



























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