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Continued from Page 6
Dear Nuts & Volts:
Generally, you have a fine publication, well written, carefully planned,
and thoughtfully layed out and, while
it was with great regret that I was witness to the demise of the Gernsback
publication Poptronics, it was worth
losing it to discover Nuts & Volts.
Where have you been all my life?
Well, enough gushing. All that
said, I discover you are subject to some
of the same problems that likely plague
all technical publications — having
to rely upon contributing authors to
supply accurate data/information with
their submissions. I refer to the strobe
light project “In the Blink of an Eye” in
the May 2005 issue. The author, Andy
Sullivan, presents erroneous data
points for the charging of an RC circuit.
He states that an RC circuit will charge
to 40% of full charge in one time constant (TC), 75% in two TCs, 90% in
three TCs, and 96% in four TCs. These
percentages, as well as his assertion
that a capacitor is fully charged after
four TCs, are incorrect. If these percentages are derived from empirical
measurements, Mr. Sullivan must have
some extremely leaky capacitors.
The true data points for charging
capacitors/RC circuits are:
1 TC = 63.7%
2 TC = 86.8%
3 TC = 95.2%
4 TC = 98.3%
5 TC = 99.3%
The charge percentages are
derived from the fact that each time
constant actually charges the same
percentage as the previous TC:
63.7%. However, each TC can charge
only 63.7% of the differential
voltage between the capacitor and
the source voltage. Example: In the
circuit in question, the source voltage
V diff. remaining
% full charge
After five TCs, the differential
voltage becomes so small as to be
inconsequential, and the amounts of
capacitance and/or duration of time
constant are irrelevant to the percentage of full charge per time constant.
I hope this has been helpful in
clarifying the RC charge cycle.
Sioux Falls, SD
Response: Thank you for taking the
time to read my submission, “In the
Blink of an Eye,” and for submitting
a response. You raise an interesting
point about charging RC circuits.
The percent of charge as a function
of time is different if you are talking
energy or voltage. Because the
strobe circuit was sized to provide
the appropriate energy to the strobe
tube, my numbers indicate the
percentage of total energy charged
in an RC time constant. Total energy
is represented as follows, where U is
the percentage of energy when fully
U ≈ (1 - e-t/RC )2
Your values represent the percentage of total voltage built during
charging. The energy charged is
proportional to the voltage squared,
as shown below where C is the
capacitance: U = 1 CV 2
Squaring your values for voltage yields my values for energy as
shown below. U = % energy
charged and V = % voltage charged.
— Andy Sullivan