Parallel RC Circuits
Inductors, Capacitors, Transformers
We're in 7-4B. In this section, we're going to take a brief look at parallel RC circuits. In the previous section, we had looked at series RC circuits, and you'll note here on our little schematic that herein lies the difference. These two components are now in parallel. In the previous diagram, they had been in series.
Parallel RC Circuits
As with series RC circuits, the techniques used with other parallel configurations may be applied to parallel RC circuits. Voltage drops in a parallel RC circuit are the same as in every other parallel circuit; and hence, they are equal. We have an applied voltage and that voltage is equally applied across the resistor and across the capacitor.
Let's see, and here we have our diagram of applied voltage and this will be the same throughout the circuit, and here we have, let's just continue here, currents in a parallel RC circuit are calculated by summing the individual branch currents using Ohm's Law, but it must be done with phasor additions since they are 90 degrees out of phase and that's addressing the relationship of the current through the resistor and the current through the capacitor. In current relationships, you might note they are 90 degrees out of phase. In this case, the current through the cap is actually leading the current through the resistor. That was not the case with the voltage, but that is the case with current.
Here we see our phasor diagram. You'll notice here we have the current through the resistor in the lower, and then here we have the current through the capacitor which is 90 degrees leading. Again, the total current is going to be the phasor current which would be calculated using the formula that we have down here. This would be IR squared plus IC squared and the square root of that value. Let's do a quick calculation here. We have, where is our little calculator, what we'll do we'll have a sample here. If branch currents were 10 microamps and 20 microamps what is the total current that is applied? If we said, let's go 10, exponent and this is going to be minus six since it is micro, and then we square that, and then we add that to 20 exponent minus six and we will square that as well, add them together, and we have 500. Then, we're going to take the square root of that and that leaves us with 22.361 microamps, 22.361, 22.361. If we had 10 microamps here and 20 microamps here, then the applied total current would be 22.361 microamps. You can see the phase relationships here regarding current. Here is the current through the resistor. Here is the current through the cap, and you'll notice that the total current is a little bit out of phase with either of these because these two are obviously out of phase and this is the resultant total current.
Parallel RC circuits continued. Impedance is calculated by applying Ohm's Law. It is most commonly done by dividing the total voltage by the total current. In the previous screen, we had calculated the total current. Here we have the applied voltage and that would give us our impedance. That is always the case that resistance equals voltage divided by current. If the total voltage is 10 volts and the total current is 35 milliamps, then total impedance is and here we have a value of 286 ohms of impedance.
The behavior of either a series or a parallel RL circuit is very similar to the characteristics for series and parallel RC circuits. A summary of RL circuit characteristics can be found in your text on 7-6, and we will not formally address them as we mentioned earlier. They will only be addressed in an abbreviated form.