Re: Series-Parallel DC RC circuit

Jon Kirwan wrote:
On Sun, 08 Mar 2009 14:25:54 -0700, John Larkin
<jjlarkin@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:

On Sun, 8 Mar 2009 14:08:03 -0700, "bg" <bg@xxxxxxxxxx> wrote:

kayvee wrote in message ...
+---------R1-------*-------*
| |
R2 C1
| |
GND------------------*-------*

Hi, I'm am interested in finding the voltage across the capacitor in
this DC circuit in time. Initially, when the capacitor is uncharged,
I know that the voltage across it is 0, and as time goes on the charge
will build and the voltage across it will as well. But, how do I
calculate the voltage across it as a function of time?

Thanks.
When you charge a capacitor from a DC source, through a resistor, the
voltage across the capacitor rises. The rise of the capacitor voltage with
time plots according to the equation -

Vc = E (1 - e^ (-t/RC))

Vc = voltage across the cap
E = applied DC voltage
e = epsilon = base of natural logarithms = 2.71828
t = elapsed time
R = resistance in ohms
c = capacitance in farads

If you make your applied voltage equal to 1, then the capacitor voltage Vc
is equal to a fraction or percentage of the applied voltage for any given
time that has elapsed. This is called a universal time constant chart. What
makes it universal, is that the shape of the curve never changes, only the
values for time and percent change.
RC is called a time constant. RC is actually equal to time in this instance.
So you can mark the X axis in units of time or RC units. The y axis is
marked in percent or as a decimal part of E applied

Now if you plot this equation -
Vc = 1 - e^ (-t/RC)
you get a universal time constant chart of the capacitor voltage expressed
as a percentage or decimal part of the applied voltage for the elapsed time
in RC units.

Examples ----
If you allowed the capacitor to charge for 1RC unit then the capacitor
voltage will rise to 63% of the applied voltage.
2 RC units = 86%
3 RC units = 95%
etc

Your circuit has a shunt resistor and a series resistor. The capacitor
charges through the series resistor, and it is the value of the series
resistor that you should use for the RC units.
No. The Thevenin equivalent resistor value sets the time constant, and
that's the equivalent value of the two resistors in parallel.

If V=1, R1=R2=1K and C=1uF, C will charge to 0.5 volts with a time
constant of 500 microseconds.

Well, he didn't specify what R was, as I read it (I may have missed
something, of course.)

I agree that the thevenin resistance is the correct value to use for the
time constant. However my reading of bg posting agrees with JL. Bg says:

"Your circuit has a shunt resistor and a series resistor. The capacitor
charges through the series resistor, and it is the value of the series
resistor that you should use for the RC units."

To me, this says that only the series resistance is used for the time constant
calculation.

.

Relevant Pages

  • Re: Simple Linear Supply (for teaching my son)
    ... I intend to start by using a 3.3k ohm resistor for the "BASE DRIVE" ... might blow just charging the storage capacitor the first time. ... two or three blocks for the voltage ... The other BJTs won't heat much on ...
    (sci.electronics.basics)
  • Re: Low pass filters
    ... > what the electrons are doing at the resistor and capacitor. ... Do you understand how a series RR voltage divider can reduce the ... flow changes the pressure difference by changing how much the membrane ...
    (sci.electronics.basics)
  • Re: 90 degree phase shift for capacitor heating
    ... Putting the capacitor to the hot line will give you a nearly 90 degree ... and pass them to the resistor with little attenuation. ... the resistor/capacitor phase shift has a voltage loss, ... technique such as an operational amplifier based circuit. ...
    (sci.electronics.design)
  • Re: Baisc resistor, electricity, and capacitor questions
    ... Do resistors resist current or voltage or both? ... or does a resistor just slow down the passage of voltage ... capacitor then LED in series with a 9V battery, ... more current will flow and the light will stop. ...
    (sci.electronics.basics)
  • Re: Where are all the ESR meters?
    ... pair of diodes to discharge the test capacitor ... common glass diode and/or a 1/4-watt resistor? ... comparator, if it is more then a few volts, have a indicator displayed to ... I think it would be far better to make a current source and voltage ...
    (sci.electronics.design)
Quantcast