ohms. At the instant that E is applied to the circuit, the current
is 0.1 mA and the applied voltage E appears across R. Since one
coulomb is the quantity of electrons required to pass a given point
in the circuit during one second of time in order to produce a
current flow of one ampere, the initial rate of charge must be 0.0001
coulomb per second (this is determined on the basis that the initial
current is 0.1 mA) or 0.0001 x 106 coulomb per usec. After 1 usec,
the voltage across C is equal to 0.0001 x 106 (charge in coulombs)
divided by 109 (capacitance in farads) or 0.1 volt. The voltage
across R, therefore, is equal to 0.9 volt and It is equal to 0.09 mA.
Since It now is equal to 0.09 mA, the rate of charge has decreased to
0.00009 coulomb per second or 0.00009 x 106 coulomb per usec. After
2 usec, Q is equal to 0.00001 x 106 + 0.00009 x 106 or 0.00019 x
106 coulomb. Ec then is equal to 0.00019 x 106/109 or 0.19 volt.
The rate of voltage change is now 0.09 volt per usec. ER, at this
time, is equal to 0.81 volt and the current is equal to 0.081 mA. In
a similar way, all values of It, ER, and Ec, and the charging rate
can be determined until the steadystate condition is reached.
PRACTICAL APPLICATIONS OF RC AND RL CIRCUITS
Section I. RELATIONSHIP BETWEEN TIME CONSTANTS AND
PULSE DURATIONS
14.
TIME CONSTANT CHARACTERISTICS.
a. In the series RC and RL circuits discussed previously, the
time required for the output current or voltages to reach a steady
state condition depended on the time constant of the circuit. Time
constants were used in describing pulse characteristics during the
rise time, duration period, or decay time of the output pulse. Time
constants are a factor in determining the amplitude of the output
pulse since it can prohibit the amplitude from reaching a value equal
to the applied voltage (Figure 21D). Time constants are also a
factor in determining the value to which the output pulse decays
since it can prohibit the pulse from decaying to zero before the next
input pulse is applied (Figure 21C).
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