# What is the capacitance of this capacitor?

Q: A thin metal plate P is inserted between the plates of a parallel plate capacitor of capacitance C in such way that its edges touch the two plates. The capacitance now becomes?

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My thoughts:

We know that the capacitance of a capacitor doesn't depend upon the charge upon it neither on the potential difference between the plates or shells. In this case, since both the plates are connected by a conductor (metal plate) the potential difference across both the plates is always $$0$$. How do I find the capacitance in this case? The answer says:

Theoretical capacitance = $$\infty$$ , because effective distance between the plates becomes zero upon joining the metal plate.

How can the capacitance be infinite? Will not there be a breakdown of the dielectric medium molecules surrounding it if the capacitance extends a certain limit? Help needed.

• The provided answer is most likely wrong. Does the question imply that the plate P is in electrical contact with the 2 armors? In such a case, your capacitor becomes just one conductor and it would make only sense to compute its capacity with respect to infinity. Aug 25 at 8:14
• so it's more of a conductor rather than a capacitor?
– Vega
Aug 25 at 8:54
• yes! Chris' answer gives a good insight into the problem. Aug 25 at 9:02

Capacitance is not a very useful concept to apply to something that is not a capacitor. If you insist on assigning a capacitance to a simple wire, though, the reasonable value is actually infinity. An ideal wire has 0 reactance at all frequencies $$\omega$$ and reactance is given by $$X=\omega L-\frac{1}{\omega C}$$. It's clear that this can only be zero for all frequencies for $$L=0$$ and $$C=\infty$$.