Nuts & Volts - July 2005

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Reader Feedback

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 is 340V.

TC 1 2 3 4 5

V cap. 216.6V 295.3V 323.8V 334.1V 337.8V

V charged 216.6V 78.5V 10.3V 3.8V 1.4V

V diff. remaining 123.4V 43.9V 16.2V 5.9V 2.2V

% full charge 63.7% 86.8% 95.2% 98.3% 99.3%

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.

Charles Rhines 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 charged:

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_CV₂