Finding Phase Difference in an RC circuit

In summary, the conversation discusses finding the admittance, current, and power in a circuit with resistors and capacitors. The solution for part a is determined to be Z = 5Ω - 3.97jΩ and Y = 1/Z. For part b, the magnitude of Z is calculated to be 6.83Ω and the current is found to be 1.57A. The power is calculated to be 6.15W. The conversation also mentions being stuck on finding the phase difference, but provides a method for calculating it using the polar notation of Vo/Vi.
  • #1
TheBigDig
65
2

Homework Statement


2f81f751582010247d94b5e5d9a53c5a.png


Homework Equations


##V = ZI##
##Z_R = R##
##Z_C = -\frac{j}{\omega C}##
##Z = \sqrt{R^2 + (\frac{1}{\omega C})^2}##
##P_{av} = \frac{1}{2}V_m I_m cos(\phi)##
##\phi = arctan(\frac{-1/\omega C}{R})##
##\Delta \phi = \phi _1 -\phi _2##

The Attempt at a Solution


I've found what I believe to be the solution to the first part ##Z_{in} = Z_R + Z_C = 5\Omega - 3.97j \Omega## and the admittance which is ##Y = \frac{1}{Z}##

For part b, I calculated the magnitude of Z and got ##Z = 6.83 \Omega ## and then found the current using ##I_m = \frac{V_m}{Z}## = 1.57A. I calculated ##\phi = -38.4^o## and got a power of ##6.15W##.

For part c, I'm stuck on finding the phase difference (##\Delta \phi##) because I'm not sure how to find another value of ##\phi## and there is none specified in the question. Any help would be appreciated.
 
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  • #2
Ii = Io = Vi/(R - j/ωC)

Vo = Io * ( -j/ωC )

Phase shift = Φ , where Φ is calculated from Vo/Vi = xxxx∠Φ ( result in polar notation )

You may find an easier way, but this is the "basic" method.
 
Last edited:

1. What is phase difference in an RC circuit?

Phase difference in an RC circuit refers to the difference in timing between the voltage and current signals in the circuit. It is measured in degrees and represents how much the current signal lags or leads the voltage signal.

2. Why is it important to find the phase difference in an RC circuit?

Understanding the phase difference in an RC circuit is important because it affects the behavior and performance of the circuit. It can help determine the frequency response and stability of the circuit, and is also used in troubleshooting and designing electronic systems.

3. How do you calculate the phase difference in an RC circuit?

The phase difference in an RC circuit can be calculated using trigonometric functions such as tangent. The formula is arctan(-1/2πRC), where R is the resistance and C is the capacitance in the circuit. Alternatively, it can also be measured using an oscilloscope.

4. What factors can affect the phase difference in an RC circuit?

Several factors can affect the phase difference in an RC circuit, including the values of the resistance and capacitance, the frequency of the input signal, and the type of circuit configuration. Temperature and other external factors can also have an impact on the phase difference.

5. How can phase difference be adjusted in an RC circuit?

The phase difference in an RC circuit can be adjusted by changing the values of the resistance and capacitance components, or by altering the frequency of the input signal. The type of circuit configuration can also be modified to adjust the phase difference.

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