Chapter 25. Capacitors. 25-2 Capacitor and Capacitance. A capacitor consists of two isolated conductors (the plates) with charges + q and - q. Its capacitance C is defined from q=CV Where V is the potential difference between the conductors. 25-3 Calculating the Capacitance.
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Where V is the potential difference between the conductors.
The plate area is A and the distance between the plates is d.
The isolated conductor is a sphere of conducting material which is isolated such that it keeps its charge. It is considered to be a spherical capacitor of an outer sphere with infinitely large radius b=∞
and substituting about b=infinity, and a=R, the radius of the inner sphere,we get
In Fig. 25-7 a, switch S is closed to connect the uncharged capacitor of capacitance C =0.25 mF to the battery of potential difference V= 12V. The lower capacitor plate has thickness L=0.50 cm and face area A=2.0 x 10-4 m2, and it consists of copper, in which the density of conduction electrons is n= 8.49 x 1028 electrons/m3. From what depth d within the plate (Fig. 25-7b) must electrons move to the plate face as the capacitor becomes charged?
Capacitor 1, with C1 =3.55 mF, is charged to a potential difference Vo= 6.30 V using a 6.30 V battery. The battery is then removed, and the capacitor is connected as in the figure to an uncharged capacitor 2, with C2=8.95 mF When switch S is closed, charge flows between the capacitors. Find the charge on each capacitor when equilibrium is reached.
The potential energy U stored in a capacitor due to holding the charge q, is given by
In case of the parallel plate capacitor, the potential energy per unit volume between the plates is given by
The capacity of this spherical conductor is given by
and the potential energy is given by
The energy density u is given by