How Do You Calculate Instantaneous Voltage Across a Capacitor in an AC Circuit?

In summary, the question involves calculating the instantaneous voltage across a capacitor in a circuit with given values of resistance, capacitance, frequency, and peak voltage of the source. The voltage is calculated at a specific time after the positive zero crossing of the current waveform. The solution involves calculating the reactance and phase shift, and then using the formula for voltage (Vc)msin(2*pi*f*t-(pi/2)) without incorporating the phase shift. Using a phasor diagram can also help in visualizing the voltage and current relationship.
  • #1
Flupps
3
0

Homework Statement



Series_RC_Circuit.jpg


For the circuit in question1above: R=(3.74x10^2) (Ω), C=(3.8700x10^-7) (F), f=(4.610x10^3) (Hz) and the peak amplitude of the voltage of the source (ES)=(6.185x10^1) (V). Calculate the instantaneous value of the voltage across the capacitor at t=(4.110x10^-5) (s) after the positive zero crossing of the current waveform.

Homework Equations



v=Vmsin(2*pi*f *t + θ)
Xc = 1/(2*pi*f*C)
θ = tan^-1(Xc/R)

The Attempt at a Solution



The part that's confusing me is where it says "after the positive zero crossing of the current waveform". I've tried using the phase shift angle and subtracting 90 degrees to put into equation:
v=Vmsin(2*pi*t + θ). I've also tried using just the phase shift angle, using only 90 degrees, and using 90 degrees + phase shift angle, and none have gotten me an answer any where near what it's supposed to be.

What I've done so far is calculated Xc = 89.2 ohms
then calculated phase shift = 13.41 degrees
then tried a number of different combinations of angles using the formula v=Vmsin(2*pi*t + θ)

Could anyone tell me where I'm going wrong? This question is driving me nuts :(

after looking at the question some more, perhaps this is what I am supposed to do?

vr = vmsin(2*pi*f*t - 13.41 degrees (0.216368996rad) = 51.16253852 V
vs = vmsin(2*pi*f*t) = 57.43068007 V

vc = vs - vr = 57.43068007 V - 51.16253852 V = 6.268 V
 
Last edited:
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  • #2
You have the voltage waveform - what is the corresponding current waveform?
(i.e. what is the relationship between voltage and current?)
 
  • #3
Isn't the capacitor voltage lagging the current by 90 deg? I'm not sure how to incorporate the phase shift though, and I've tried this question a few more times and still end up with an answer that's way off.
 
  • #4
The phase shift comes out automatically if you use complex impedances ... if you are just using reactances, you should use a phasor diagram: the loop law voltages add head-to-tail.
 
  • #5
Ah thanks! With the same problem with different numbers I had R = 350, C = 380nF, f = 3.91kHz, (Es)m = 29.86v

Got an answer of -3.12v which was correct.

It became much simpler now that I know the phase shift isn't used... just used formula (Vc)msin(2*pi*f*t-(pi/2)) after calculating the other stuff and it gave me the right answer

Thanks for the help!
 

Related to How Do You Calculate Instantaneous Voltage Across a Capacitor in an AC Circuit?

1. How do I approach solving an AC circuit problem?

The first step in solving an AC circuit problem is to draw a circuit diagram. This will help you visualize the components and their connections. Next, label all known values and unknown variables. Then, apply Kirchoff's laws and Ohm's law to write equations for the circuit. Finally, solve for the unknown variables using algebraic manipulation or by using a calculator.

2. What is the difference between AC and DC circuits?

The main difference between AC (alternating current) and DC (direct current) circuits is the direction of the current flow. In AC circuits, the current changes direction periodically, whereas in DC circuits, the current flows in one direction. AC circuits also have the ability to vary in amplitude and frequency, while DC circuits have a constant amplitude and frequency.

3. How do I calculate the impedance in an AC circuit?

To calculate the impedance in an AC circuit, you can use the formula Z = R + jX, where R is the resistance, j is the imaginary unit, and X is the reactance. The reactance can be further broken down into capacitive reactance (Xc) and inductive reactance (Xl). The total impedance is then the square root of the sum of the squares of the resistance and the reactance.

4. What is the significance of phase in AC circuits?

In AC circuits, the phase refers to the relationship between the voltage and current waveforms. It is measured in degrees and represents the time delay between the two waveforms. The phase is important because it affects the overall power and efficiency of the circuit. A phase difference between the voltage and current can also lead to power factor loss.

5. How do I incorporate complex numbers in solving AC circuit problems?

In AC circuits, complex numbers are used to represent the amplitude and phase of the voltage and current. To incorporate complex numbers in problem-solving, you can use the polar form of complex numbers, where the amplitude is represented by the magnitude and the phase is represented by the angle. You can then use the properties of complex numbers to manipulate the equations and solve for the unknown variables.

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