Capacitor having equal charges on plates connected to a battery

  1. Hello

    I am having a doubt regarding capacitors .I know that when two neutral plates of an uncharged capacitor of capacitance C are connected to a battery of V volts then charges present on the inner surface of the plates are equal and opposite i.e +Q and -Q,where Q=CV .

    But what will happen when both plates are initially having a positive charge +q and then a battery of V Volts is applied across the plates ?

    My doubts are

    1)In general a battery supplies equal and opposite charges.Does the battery supply equal and opposite charges in this case too ,where the plates are already having +q on them ?

    2) If the inner surfaces of plates of the capacitors have equal and opposite charges after the battery is connected ,then in this case the outer surfaces will carry unequal charges . Is it so ?

    Please clarify my doubts ...Thanks
     
  2. jcsd
  3. mfb

    Staff: Mentor

    That will not happen in a significant way in electronics. Usually, all parts are so close to neutral that you can neglect net charges. In addition, that charge would be on the outside, not on the inner side of the capacitor.
    Your charges would be distributed over the whole setup, in addition to the +Q, -Q on the inner sides of the capacitor.
     
  4. sophiecentaur

    sophiecentaur 13,698
    Science Advisor
    Gold Member

    A 'typical' capacitor could well have a high capacitance (1μF) between its plates but its capacitance to ground will be no more than a few pF. You would need to charge the whole capacitor up to a voltage almost one million times higher than the volts between the plates for the total (unbalanced) charge to be the same as the (balanced) charge difference 'inside' it.

    The formula Q = CV applies in both cases.

    In RF circuits, where small values of capacitor (only a few pF) are often used, the total charge on a capacitor may well be on the same order as the charge stored (during an RF cycle) between the plates.
     
  5. Does a battery always supply equal and opposite charges to plates of a capacitor irrespective to whether the plates are neutral or they may have charge on them initially (say +q charge on both plates initially before the battery was connected )?
     
  6. sophiecentaur

    sophiecentaur 13,698
    Science Advisor
    Gold Member

    If the battery is in series - directly - with the two sides of the Capacitor then, of course, the same charges must flow in and out of the terminals of the capacitor.
    But it is quite possible for a capacitor to have an excess +charge on both of its terminals. Just stick a series capacitor / battery circuit on top of a Van der Graaff generator globe, if you want an extreme example. There will be a net charge all over that circuit with the C 'charged up' by the battery PD.
     
  7. Hello sophiecentaur!!!

    Thanks for the response...Sorry for responding late ...

    Does that mean that the inner surface of the capacitor will have equal and opposite charges and the outer surface of the plates will carry unequal positive charges ( since both the plates are initially having a positive charge +q before the battery of V Volts is applied across the plates ) ?
     
  8. sophiecentaur

    sophiecentaur 13,698
    Science Advisor
    Gold Member

    I would guess that, as the spacing between the capacitor plates is so small that the field would be high enough to dominate and that what you suggest is probably right. But imagine taking the model to an extreme, consisting of two charged objects (which were, 'preciously', the capacitor plates) separated by a significant distance and above a 'ground'. Then give the two objects different charges by giving them, independently, a different Potential wrt ground. The distribution of the charges around the objects would depend both upon their actual separation and their distance from the Ground - they wouldn't all rush to the nearest points on the two objects, would they?
    The other extreme could be two capacitors connected in series and the end of one is connected to ground. One is charged (with a floating supply) and then the other. . . . . . .?
     
  9. Thanks a lot ...
     
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