Capacitance and Condensers
When a positively charged body is brought near the end of an uncharged metal rod, the near end of the rod becomes negatively charged and the far end becomes positive. The rod is said to be charged by induction. The electrical charges at the ends of the rod are called " induced charges." They are numerically equal to each other. When the original charged body is removed, the rod becomes neutral again.
Figure 3 B shows a source of electricity at E (the battery), connected by two metal wires to two metal plates, A and B. The two plates together with the insulating air between them, are called a condenser. Let Q be the amount of electricity on plate A, which is also equal numerically to the opposite charge on plate B. It is found that Q will be larger, and in direct proportion, if the battery voltage E is larger. This fact can be expressed by the equation Q = CE, where C is a constant, called the capacitance of the condenser. Imagine a tank filled with water to a depth of 1 foot. This amount of water is the " capacity " of the tank, in the sense used above (quantity stored under unit potential). Of course the condenser will hold more electricity than the unit amount, C; in fact, it will hold a total of E times the unit amount, just as the water tank will hold water clear up to its top. The " top " point of the condenser is the breakdown point of the insulator. If the voltage E is too great, the condenser will be ruptured and an electrical spark will occur between the plates.
The capacitance C depends on the area of the plates, their separation, and upon the kind of insulator between them. The capacitance will be greater if glass or mica is used as the insulator instead of air. The amount by which the capacitance exceeds the air (or, more accurately, the vacuum) value, is called the dielectric constant of the insulator. Some dielectric constants and breakdown voltages are given in Table 3 A.
The unit of capacitance is called the farad. A condenser is said to have a capacitance of one farad if one coulomb is stored in it under a potential difference of one volt. This can be done by allowing a current of one ampere to flow into the condenser for one second. It is a very large unit. The following, more convenient, units are used in electronics: (1) the microfarad, abbreviated μfd, which is one one-millionth (10-6) of a farad, and (2) the micro-microfarad (10-12), abbreviated μμf.
The capacitance of a series combination of condensers can be computed by the formula in Fig. 3 C.
The capacitance of a parallel combination of condensers is calculated from the formula given in Fig. 3 D.
The capacitance of a plane parallel plate condenser is given by,
where k is the dielectric constant, A is the area of one of the plates in square centimeters,
and d is the distance between the plates in centimeters.
Basic Radio, Author: J.B. Hoag