Tab Electronics Guide to Understanding Electricity ... - Sciences Club

Capacitance
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In reference to capacitors, the short would occur through the dielectric,
destroying the capacitor in the process).
As the graph in Fig. 5-2 illustrates, the capacitor in the circuit of Fig. 5-1
charges exponentially. This means that it charges in a nonlinear fashion. An
exponential curve (like the charge curve in Fig. 5-2) is one that can be
expressed mathematically as a number repeatedly multiplied by itself. The
exponential curve of the voltage across a charging capacitor is identical to
the exponential curve of the current increase in an LR circuit as shown
in Chapter 3 (Figs. 3-5 and 3-6).
As discussed in Chapter 3, the current change in an LR (inductiveresistive)
circuit, relative to time, is defined by the time constant and
expressed in seconds. Similarly, in an RC (resistive-capacitive) circuit, the
voltage change across the capacitor is defined by the time constant, and
it is also expressed in seconds. An RC time constant is defined as the
amount of time required for the voltage across the capacitor to reach a
value of approximately 63% of the applied source voltage. The RC time
constant is calculated by multiplying the capacitance value (in farads)
times the resistance value (in ohms). For example, the time constant of
the circuit shown in Fig. 5-1 would be
Tc RC (1,000,000 ohms) (0.000,001 farad) 1 second
The principle of the time constant, that applies to inductance, also
applies to capacitance. During the first time constant, the capacitor
charges to approximately 63% of the applied voltage. The capacitor in
Fig. 5-1 would charge to approximately 6.3 volts in one second after SW1
is closed. This would leave a remaining voltage differential between the
battery and capacitor of 3.7 volts (10 volt 6.3 volts 3.7 volts). During
the next time constant, the capacitor voltage would increase by an additional
63% of the 3.7-volt differential; 63% of 3.7 volts is approximately
2.3 volts. Therefore, at the end of two time constants, the voltage across
the capacitor would be 8.6 volts (6.3 volts 2.3 volts 8.6 volts). Five
time constants are required for the voltage across the capacitor to reach
the value usually considered to be the same as the source voltage.
In the circuit shown in Fig. 5-1, the approximate source voltage
(10 volts) would be reached across the capacitor in 5 seconds. If SW1 is
opened, after C1 is fully charged, it would hold the stored energy
(1 microfarad) at a 10-volt potential for a long period of time. A “perfect”
capacitor would hold the charge indefinitely, but in the real world, perfection
is hard to come by. All capacitors have internal and external leakage
characteristics, which are undesirable. It would be reasonable,