Capacitance and Capacitors

Recall heat capacity (c) –The amount of heat energy (J) absorbed (released) by a material of known mass (m) when changing temperature (  T) with no phase change

Electrical capacitance Defined as the amount of charge per volt that an object can hold

Anything can be a capacitor The capacitance is defined as Q/V, but it is also solely dependent on the geometry of the capacitor. There should be an equation for the capacitance that is based only on the physical dimensions of the capacitor. The capacitance is measured in farads (F) after Michael Faraday

Example 1: A charged sphere of radius R If the charge on the sphere is Q, the potential at the surface is V = kQ/R The capacitance is then

Example 2: Parallel plate capacitor When the plates are charged, one plate has charge +Q, and the other -Q, so we say that the charge on the capacitor is Q. For parallel plates,  V = Ed and E =  0, where  = Q/A is the charge density on the plates, so

Dielectric Adding a material to the space between the plates changes the capacitance of the capacitor

Table 20-1 Dielectric Constants Substance Dielectric constant,  Water80.4 Neoprene rubber6.7 Pyrex glass5.6 Mica5.4 Paper3.7 Mylar3.1 Teflon2.1 Air Vacuum1

Capacitors in series Adding capacitors in series, V tot = V 1 + V 2, so The charge on each capacitor must be the same when they are connected in series… Why?

Energy in capacitors W = q  V ave

Capacitors in parallel Adding capacitors in parallel, V tot = V 1 = V 2, so

Sample problem

Charging capacitors in RC circuits When switch is first closed, uncharged capacitor acts like a wire, with no voltage drop across it (t = 0) After a long time, once the capacitor is fully charged, it acts like an open switch (t  infinity) When switch is first closed on a charged capacitor, it acts like a battery