# RC circuit question: In vs. Out phase angle

• Habeebe
In summary: Both the change in amplitude and the phase shift are the result of the ratio of the real impedance of the resistor and the "imaginary" impedance of the capacitor (which varies with frequency). It's easiest to show it by using the math, but another way to think about it is that you are temporarily storing energy in the capacitor voltage with each swing of the AC waveform, whereas you are always just dissipating the energy with the voltage across the resistor. So, when the input voltage is at a higher frequency than the resonant frequency of the circuit, the capacitor will be charging and discharging more frequently, and this will cause the output voltage to swing more in response to the input, with a bigger amplitude swing.
Habeebe
In an RC circuit, the phase angle between the input and output voltages (not current and voltage) seems to be proportional to the amplitude of the output voltage. That is, as the phase angle between input and output goes to plus or minus 90 degrees, the output voltage goes to 0. Why is that?

Habeebe said:
In an RC circuit, the phase angle between the input and output voltages (not current and voltage) seems to be proportional to the amplitude of the output voltage. That is, as the phase angle between input and output goes to plus or minus 90 degrees, the output voltage goes to 0. Why is that?
Hi Habeebe. Phase does not vary with amplitude of the input. But output amplitude and phase are both frequency-dependent, so over a limited range there may be a roughly linear correspondence. What are the equations you have where you are interpreting there is such a correspondence?

Last edited:
Experimentally. I'm not getting it from equations. If you have a high pass filter, and you run the input voltage to a low frequency, the phase angle will go to about 90 degrees between input and output while the output voltage goes to some small amount. I don't know or really care about the exact relation between the two numerically, but it appeared as though that phase angle difference was somehow related to the change in output voltage. I'm really more interested in what physically is going on that both things happen together.

Habeebe said:
Experimentally. I'm not getting it from equations. If you have a high pass filter, and you run the input voltage to a low frequency, the phase angle will go to about 90 degrees between input and output while the output voltage goes to some small amount. I don't know or really care about the exact relation between the two numerically, but it appeared as though that phase angle difference was somehow related to the change in output voltage. I'm really more interested in what physically is going on that both things happen together.

Both the change in amplitude and the phase shift are the result of the ratio of the real impedance of the resistor and the "imaginary" impedance of the capacitor (which varies with frequency). It's easiest to show it by using the math, but another way to think about it is that you are temporarily storing energy in the capacitor voltage with each swing of the AC waveform, whereas you are always just dissipating the energy with the voltage across the resistor.

Think of a resonant system that you excite off of resonance. Like a ball on a spring -- if you wiggle the end of the spring at a frequency that is not the natural resonant frequency of the ball+spring system, then the ball will often move with a phase shift compared to how you are wiggling the spring.

Anyway, here is a typical RC lowpass plot like the behavior you are describing:

https://www.library.cmu.edu/ctms/ctms/matlab42/freq/bode1a.gif
https://www.library.cmu.edu/ctms/ctms/matlab42/freq/bode1a.gif

The phase angle between the input and output voltages in an RC circuit is determined by the relationship between the resistance (R) and capacitance (C) of the circuit. This relationship is known as the impedance (Z) and is represented by the formula Z = R + 1/jωC, where j is the imaginary unit and ω is the frequency of the input voltage.

When the phase angle between the input and output voltages is at plus or minus 90 degrees, it means that the impedance of the circuit is purely reactive, with no real component. This occurs when the frequency of the input voltage is equal to the resonant frequency of the circuit, which is determined by the values of R and C.

At this frequency, the reactance of the capacitor (1/jωC) cancels out the resistance (R), resulting in a purely imaginary impedance. This leads to a phase shift of 90 degrees between the input and output voltages. Since the output voltage is determined by the ratio of the impedance to the input voltage, a purely imaginary impedance will result in an output voltage of 0.

In summary, the relationship between the resistance and capacitance in an RC circuit determines the impedance and therefore the phase angle between the input and output voltages. At the resonant frequency, the impedance becomes purely reactive, resulting in a phase shift of 90 degrees and an output voltage of 0. This phenomenon is known as resonance and is a fundamental property of RC circuits.

## 1. What is an RC circuit and how does it work?

An RC circuit is a type of electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series or in parallel. The resistor and capacitor work together to control the flow of electric current in the circuit. When a voltage is applied to the circuit, the capacitor charges up to the same voltage as the source, while the resistor limits the flow of current. As the capacitor charges, it creates an electric field, storing energy in the circuit. Once the capacitor is fully charged, it can discharge and release the stored energy back into the circuit.

## 2. What is the phase angle in an RC circuit and how is it measured?

The phase angle in an RC circuit refers to the difference in timing between the voltage and current in the circuit. It is measured in degrees or radians and indicates how much the current leads or lags behind the voltage. A phase angle of 0 degrees means that the current and voltage are in phase, while a phase angle of 90 degrees means that the current lags the voltage. The phase angle can be measured using an oscilloscope or calculated using mathematical formulas.

## 3. How does the phase angle affect the behavior of an RC circuit?

The phase angle has a significant impact on the behavior of an RC circuit. A phase angle of 0 degrees means that the current and voltage are in phase, and the circuit behaves like a simple resistor. As the phase angle increases, the circuit starts to exhibit more complex behavior, such as frequency-dependent impedance and energy storage. This can lead to phenomena like resonance and filtering, making the phase angle an essential aspect to consider in RC circuit design and analysis.

## 4. What is the difference between in-phase and out-of-phase RC circuits?

In-phase and out-of-phase are two terms used to describe the relationship between the voltage and current in an RC circuit. In an in-phase circuit, the voltage and current are in sync, with a phase angle of 0 degrees. This means that the current and voltage peaks occur at the same time and have the same amplitude. In an out-of-phase circuit, there is a time difference between the current and voltage peaks, with a phase angle other than 0 degrees. This indicates that the current and voltage are not in sync and have different amplitudes.

## 5. How do I calculate the phase angle for an RC circuit?

The phase angle of an RC circuit can be calculated using the following formula: φ = arctan(1/ωRC), where φ is the phase angle in radians, ω is the angular frequency (2πf) in radians per second, R is the resistance in ohms, and C is the capacitance in farads. Alternatively, you can also use a graph or an oscilloscope to measure the phase angle visually. Additionally, there are online calculators and software programs available that can calculate the phase angle for you using input values for R, C, and frequency (f).

Replies
4
Views
3K
Replies
27
Views
2K
Replies
9
Views
2K
Replies
7
Views
2K
Replies
1
Views
1K
Replies
41
Views
4K
Replies
4
Views
9K
Replies
77
Views
6K
Replies
4
Views
625
Replies
4
Views
2K