6. Capacitance and capacitors 6.1 Capacitors +Q -Q +Q -Q +Q 6.2 Capacitance [C]= 1 F = 1 C / V Definition:Units: Symbol: C is independent from: Q and ΔV (ΔV is always proportional to Q) C depends on: the geometry of the system the dielectric between the conductors

6.3 Parallel plate capacitor -Q +Q d a b 6.3a Cylindrical capacitor: 6.3b Spherical capacitor: Large plates of area A separated by a small distance d, can be considered as infinite planes.

Example (Variable capacitor): A parallel plate capacitor is connected to a battery that produces a constant potential difference across its plates. If we push the plates of the capacitor together so that the distance between them is halved, the charge on the capacitor changes by: battery -+-+ C d  d/2 V - const Q = CV C  2C Q  2Q A. ½B. 1C. 2 Example: Now, we disconnect the capacitor from the battery, and then push the plates together so that the distance between them is halved. What happened with charge and with potential difference between plates?

6.4 Capacitors with dielectrics +Q-Q -q +q If V=const The molecules in a dielectric tend to become oriented in a way that reduces the external field. 6.5 Dielectrics Overall, there is a slight accumulation of positive charge on one side and negative on the other side, but it’s much smaller than in conductors (with induction)

What happens if you bring a charged rod near a neutral insulator? Glass of pure water H H O “Normal” molecule of water Charges are not free to move. They can move a little… Molecule of water near a positively charged rod (polarized molecule) Glass of polarized pure water Positive Negative Neutral

6.6 Energy stored in an electric field a) Energy stored in a capacitor V +Q -Q b) Energy density

6.7 Capacitors in parallel C2C2 C1C1 +Q 1 Q1Q1 +Q 2 Q2Q2 A●A● B●B● C eq A ● B ● +Q eq  Q eq

6.8 Capacitors in series And remember that: Note that Use series connection to decrease capacitance C1C1 C2C2 C3C3 …

A C D Example: Which of the circuits has the largest capacitance? All capacitors are identical. B

A.3.33 pF B.6.67 pF C.15.0 pF D.30.0 pF E.All of the above Example: Which of the following capacitances can be achieved with series or parallel combinations of three 10 pF capacitors? See previous slide!