Lecture Text Capacitive RC Circuits
Troubleshooting RC circuits.
I rarely stopped probing a circuits that I was troubleshooting
to do calculations with pencil and paper. The one exception to this rule
was that I frequently used this slide rule calculator to calculate the
impedance of a capacitor or inductor. This handy slide rule calculator
made it easy for me to calculate the reactance of coils and capacitors at a
particular frequency. Today these slide rules may be collectors
items. I have provided you with a link to online calculators of impedance
and resonant frequency. See link below. I have also provided links
to a few of my circuit animations. Those of you who read and performed
troubleshooting exercises in my e-book, "Electronic Concepts" may find these animations redundant. You don't have to use the online calculator if you
have a programmable calculator that you can use to execute any formula or
sequence of formulas you desire. I consider JavaScript the official
program for this site and I teach it on my JavaScript site. JavaScript is
available on most Computers and can be developed with Note Pad and with Microsoft
Internet Explorer. Of course a JavaScript development platform is also available on Netscape.
Once you calculate the impedance of a
capacitor in ohms for a particular frequency, you will be able the view circuits
and voltage dividers in terms of components measured in ohms. Of course we
must consider the phasor nature of the components. Thus, the sum of a 10
ohm capacitance reactance in series with 10 ohm resistor is simply their vector
sum (14.14). The impedance of a ten ohm resistor in series with a 10 ohm
resistor would have been 20 ohm. In the case of a 10 ohm capacitor reactance
and 10 ohm resistor in parallel, we can use conductance to analyze the circuit .
Conductance is the reciprocal of resistance. The reciprocal of 10 is
.1. The vector sum of the resistor conductance and the capacitor
conductance is .1414 . The reciprocal of
.1414 is 7.07 . Thus the total impedance of the 10 ohm resistance and the 10
ohm capacitance reactance in parallel is 7.07 ohms rather than the 5.0 ohms
that two 10 ohm resistors in parallel would produce. Of course you could
use the Pythagorean theorem to calculate the series impedance of any pair of reactance's.
When we study transistor amplifiers in later lessons, you will see that a
resistor and capacitor in parallel are used in transistor emitter circuits to
effect the frequency response of the amplifiers. I have created circuit
animations of amplifiers that illustrate this. (Check links at bottom of
page.) A resistor and capacitor in series also makes a simple inexpensive high pass or low pass
filter.
Troubleshooting circuit failures.
Circuits usually fail in a manner
that causes a significant change in performance. Thus, if you only have a
rough estimate of how a circuit should perform, the deviation caused by
the failure of a resistor or a capacitor is usually quit noticeable to a
troubleshooter. Therefore, rough approximations of circuit performance (made in ones head) are often all that is required for troubleshooting a circuit.
