Lecture #8 Electric dipoles. Dielectrics. Electric Capacitance and Capacitors

The ratio of q/A is called the surface charge density, usually denoted by . Thus the magnitude of the field is

3.Capacitors in Combination

Let's add in the circuit the capacitor. We learned before that capacitance is proportional to the area of the plates of a parallel-plate capacitor. Thus if we could double the area we would double the capacitance.

Capacitors in Series
and Parallel
A first addition rule for capacitors
The equivalent capacitance of two capacitors connected in parallel is the sum of the individual capacitances.
Cpar = C1 + C2 + ... + Cn
The voltage V supplied by the battery appears across each capacitor. The charge on each capacitor depends on this voltage, and the capacitance of each is determined from the equation С = q/V.
All of the capacitors must
have the same voltage V:
V1 = V2 = V3= V
Capacitors connected in parallel

Capacitors in Combination (parallel)

(a) Three capacitors connected in parallel. The voltage is the same across each capacitor. (b) Schematic representation of three capacitors connected in parallel

Capacitors connected in series

Suppose instead of joining the capacitors in parallel we join them end-to-end in series across the battery (see the picture on the next slide).

The first capacitor becomes charged, it induces an equal charge in the second capacitor, which in turn induces an equal charge in the third capacitor.

All of the capacitors must
have the same charge q:
q1 = q2 = q3= q

Capacitors connected in series. The magnitude of the charge is the same on each plate of each capacitor. (That is, there is no net charge in the region marked by the colored rectangle).