A question I came across asks about two concentric spherical conductors where only the inner sheet is charged. The question first asks to find the capacitance of such an arrangement. The first part of this question seems relatively easy. I can find the capacitance of such a capacitor by first finding the voltage difference between the two plates. Since the capacitance of a capacitor is determined only by the geometric configuration of the capacitor, this should be possible. However, after finding the voltage, to find the capacitance I would usually use the formula:
C = Q/V
Does this still work when q refers to the charge on just one plate? Also does this sort of a capacitor actually store energy. If so can the equation
be used to calculate it. The final part of the question asks you to find the time taken for the voltage across the capacitor to fall to half it's original value when connected in series to a circuit with a resistor. Can the RC equations like:
q = Q(e^-t/RC)
still be used. Also, the question includes the gives the charge on the capacitor. Is this not extraneous information, since neither R nor C are affected by it? Extra points for anyone who shed some light on the physical/intuitive meaning of what is going on here?