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March/April 2014 Marine Electronics Journal 19
Energizing a capacitor across a voltage source will charge the capacitor to the value of the voltage source almost instantly. When you add a resistor in series with the capacitor you can control the amount of time it takes for it to reach the source value. The higher the value of the resistor the longer it takes to charge; this can also be done by increasing the size of the capacitor. This is done by limiting the current, increasing the time for the capacitor to reach the source voltage value. During this
charge time the current flowing from the source voltage will gradually decrease from its initial value—the capacitor electric field offers increasing opposition to the source voltage.
By Hugh Lupo, NMEA Director
During the charging period the voltage across the capacitor terminals is an exponential
function of time, and represented by the formula.
Theoretically, the charging process never completes, but the charging current will drop to
a very low, almost immeasurable, level. At this time the capacitor is at full charge. We can
represent this by letting t = RC. We can use the formula below to represent this.
The product of R in ohms times C in farads is called the time constant of the circuit and
is the time in seconds required to charge the capacitor to 63.2% of the source voltage value,
one time constant period. The symbol τ (tau) is used to represent one time constant period
in electronic circuits.
After two time constant periods (t = 2τ) the capacitor charges another 63.2% of the difference between the capacitor voltage at one time constant and the source voltage, for a total
charge of the capacitor voltage to 86.5%. After the third time constant the capacitor charge
will reach 95% and after five RC time periods the capacitor will reach 99.5% of the source
voltage, which is about the maximum you can charge to. The graph below shows this process.
If you apply a short across the leads of the charged capacitor you will discharge the
capacitor instantly. As you increase the resistance across the capacitor the time will increase.
Also, if you use a large capacitor you can store more energy and increase the time for a given
resistance. The resistor, R, limits the current, so the capacitor voltage decreases only as rapidly as the capacitor can discharge itself through R. This reacts the same way as the charging
circuit did. The discharge will go through the same time constants as the charging constants
until it reaches five time constant periods and discharges to 99.24% of its stored voltage.
This circuit is used in large high-voltage power supplies to discharge the capacitors when
the system is off. They also use it to control the inrush current in large power supplies to keep
the surge current limited when energized.
At the end of the day, with the entire math in this article, it comes down to one simple
formula: t = RC t = time in sec. R = ohm C = farads.
Next issue: Alternating current in capacitance (capacitive reactance)
V(t) = capacitor voltage in volts at time t
E = potential of charging source in volts
t = time in seconds after initiation of charging current
e = natural logarithmic base = 2.718
R = circuit resistance in ohms
C = capacitance in farads
RC Time Constant
V(RC) = E = 0.632 E 1 – e -1 ( )
RC Discharge. If a resistor is placed across the leads of a charged capacitor the time of
discharge can be controlled. The larger the value of the resistor for a known value of a capacitor will increase the time to discharge. See graph.
0 τ 2τ 3τ 4τ 5τ
1.8% 5% 0.7%
0 τ 2τ 3τ 4τ 5τ
(τ = R*C)