Q: "Why is the total (equivalent) capacitance of a series connection always smaller than each of the capacitors connected in series?" A: Look at a simple example when only two capacitors are connected in series. Then, the formula for the total (equivalent) capacitance is: You can verify that C_{eq} is less than any of the capacitors connected in series by trying the case of three capacitors, or four capacitors, etc. Do the algebra correctly, and you will always obtain C_{eq} expressed as the product of any of the individual capacitors and a factor that is less than 1 (a ratio with the denominator larger than the numerator). 
Q: What does an electrical capacitor store? A: An electrical capacitor stores a "charge Q." An electrical capacitor is defined as two conducting components separated from each other and charged with different amounts of charge, Q_{1} and Q_{2}. The "charge stored in a capacitor", Q, is the charge imbalance between the two components: Q = Q = Q_{2}  Q_{1}. It is also correct to say that an electrical capacitor stores energy. Since the two conducting components of the capacitor are charged with different amounts of charge, Q_{1} and Q_{2}, an electric field exists between them, and an electric field stores energy within the space in which the electric field exists (within the volume in space defined by the geometric arrangement, with respect to each other, of the two conducting components of the capacitor.) 
Q: Many electronic devices carry a warning that removing the case, even with the power turned off, may cause electric shock. Does this have anything to do with capacitors? Why don't they discharge as soon as the power is cut? A: When the power of the circuit is turned off, capacitors may remain charged because not all electrodes are grounded. If one touches the charged electrode one receives an electric shock caused by the discharge of this electrode through the human body. 
Q: Is it possible to break a capacitor by placing to much charge on it? A: Yes. To place too much "charge" on a capacitor means to establish a too high potential difference, V, between its conducting components. If this potential difference is above what is called "breakage potential," an electric discharge results, destroying the capacitor. If the capacitor contains an insulator between its conducting components, the insulator will be "burnt" at the atomic/molecular level. A capacitor subjected to voltages exceeding the "breakage potential" cannot be recovered. It should be discarded and replaced. The value of the "breakage potential" is given on a label attached to commercially available capacitors. 
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Capacitance 
C = q/V 
Capacitance for a parallelplate capacitor 

Capacitance for a cylindrical capacitor 

Capacitance for a spherical capacitor 

Capacitance of an isolated sphere 
C = 4 _{ 0}R 
Equivalent capacitance of capacitors connected in parallel 

Equivalent capacitance of capacitors connected in series 

Electric potential energy of a charge capacitor 

Energy density (potential energy per unit volume) 
u = _{ 0} E^{2} 
Gauss' Law with a dielectric 

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