Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Nowhere do I mention the plate "with the positive charge"
The + sign does not imply that this plate will be positively charged. The + and - charge signs merely serve to define the charge configuration to be represented by a positive value of Q, even though Q can be + or -.
This is the same approach that we use when we draw a directed arrow to define the direction of a current to be represented by a positive value of i, even though i can be + or -.
we draw a directed arrow to define the direction of a current to be represented by a positive value of i, even though i can be + or -.
In the general, complex circuit case one does not know ahead of time the directions of currents or the charge configurations of capacitors. This is true even in simple, one-loop circuits if one does not yet know the initial conditions. The equations should be written for the general case: as a computer algorithm applicable to any and all initial conditions. One therefore needs a general set of defining conventions for correlating current directions and capacitor charge configurations with the algebraic signs of the quantities i and q, respectively.
One safe way to do this is to:
1) For each current, choose (and indicate) a definite direction to be represented by a positive value of the signed variable i(t).
2) For each capacitor, choose (and indicate) one of its two plates to be that whose absolute charge is represented by the (signed) value of a variable q(t). The other plate of this capacitor will carry the absolute charge - q(t).
All of these choices are completely arbitrary. However, once chosen, they will force one or the other of the relations i=dq/dt or i=-dq/dt in the wires directly connected to each capacitor.