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# Capacitance Help (page 2)

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## The Unit Of Capacitance

When a battery is connected between the plates of a capacitor, it takes some time before the electrical field reaches its full intensity. The voltage builds up at a rate that depends on the capacitance. The greater the capacitance, the slower is the rate of change of voltage in the plates.

The unit of capacitance is an expression of the ratio between the amount of current flowing and the rate of voltage change across the plates of a capacitor. A capacitance of 1 farad , abbreviated F, represents a current flow of 1 ampere (1 A) while there is a potential-difference increase or decrease of 1 volt per second (1 V/s). A capacitance of 1 F also results in 1 V of potential difference for an electric charge of 1 coulomb (1 C).

The farad is a huge unit of capacitance. You’ll almost never see a capacitor with a value of 1 F. Commonly employed units of capacitance are the microfarad (μF) and the picofarad (pF). A capacitance of 1 μF represents 0.000001 (10 −6 ) F, and 1 pF is 0.000001 μF, or 10 −12 F.

## Capacitors In Series

With capacitors, there is rarely any significant mutual interaction. At very high ac frequencies, however, interelectrode capacitance can sometimes be a problem for engineers. This effect, which shows up as an inherent tiny capacitance between wires that run near and parallel to each other, is almost always undesirable in practical circuits.

Capacitors in series add together like resistors or inductors in parallel. If you connect two capacitors of the same value in series, the result is half the capacitance of either component alone. In general, if there are several capacitors in series, the composite value is less than that of any of the single components. It is important that you always use the same size units when determining the capacitance of any combination. Don’t mix microfarads with picofarads. The answer you get will be in whichever size units you use for the individual components.

Suppose that you have several capacitors with values C 1 , C 2 , C 3 ,..., C n connected in series (Fig. 15-6). You can find the reciprocal of the total capacitance 1/ C using the following formula:

1/ C = 1/ C 1 + 1/ C 2 + 1/ C 3 + ... + 1/C n

The total capacitance C is found by taking the reciprocal of the number you get for 1/ C .

Fig. 15-6 . Capacitances in series add like resistances or inductances in parallel.

#### Problem 1

Two capacitors, with values of C 1 = 0.10 μF and C 2 = 0.050 μF, are connected in series. What is the total capacitance?

#### Solution 1

Using the preceding formula, first find the reciprocals of the values. They are 1/ C 1 = 10 μF −1 and 1/ C 2 = 20 μF −1 . (“Reciprocal microfarads” don’t have any practical meaning, but using them can help us remember that we must take the reciprocal of the sum of the numbers before we come up with capacitance.) Then

1/ C = 10 μF −1 + 20 μF −1 = 30 μF −1

C = 1/30 μF −1 = 0.033 μF

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