Mixed parallel & series RLC circuit

[mrmlica]

Homework Statement

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Calculate impedance , current and power factor

Homework Equations

The Attempt at a Solution

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First we solve parallel part. In parallel resistor and inductor are sharing voltage. Using phasor diagrams we found vector I_1 which is current in parallel part. Series circuit share current so I have attached phasor diagram for capacitor to I_1 (as you can see). Now i need to find vector V_S which is V_C + V_R. But i don't know how to find it.

(sorry for the pics)

 

[Sleepy_time]

Hi mrmlica. Not too sure what you're trying to do, but the equivalent impedance of a parallel circuit is just: $\frac{1}{Z_p}=\frac{1}{Z_1}+\frac{1}{Z_2}+...$ and for series is: $Z_s=Z_1+Z_2+...$. Where Z is the complex impedance, Z_n is the n'th component in the given circuit, s=series & p=parallel. To find the current you use Ohm's law as you know the input voltage and the impedance. The power factor is the cosine of the phase angle between the current and the voltage. The tangent of the phase angle can be found from the argument of the complex impedance.

 

[mrmlica]

Hi mrmlica. Not too sure what you're trying to do, but the equivalent impedance of a parallel circuit is just: $\frac{1}{Z_p}=\frac{1}{Z_1}+\frac{1}{Z_2}+...$ and for series is: $Z_s=Z_1+Z_2+...$. Where Z is the complex impedance, Z_n is the n'th component in the given circuit, s=series & p=parallel. To find the current you use Ohm's law as you know the input voltage and the impedance. The power factor is the cosine of the phase angle between the current and the voltage. The tangent of the phase angle can be found from the argument of the complex impedance.

I wasnt hoping for that good help. You didnt just solve me task, you learn me new diffrent way to look on AC current. Thank you alot.

 

[Sleepy_time]

You're welcome. I'm glad I could help you with the problem in a different method to what you normally do. If you're finding any difficulty with my method just ask any questions you want to.

 

[Nickie]

Thank you for your question. In order to find the total impedance of a mixed parallel and series RLC circuit, you will need to use the following formula:

Z_total = sqrt( (R + R_p)^2 + (X_L - X_C)^2 )

Where R is the resistance of the series branch, R_p is the equivalent resistance of the parallel branch, X_L is the reactance of the inductor, and X_C is the reactance of the capacitor.

To find the current in the circuit, you can use Ohm's Law: I = V/Z_total, where V is the voltage across the circuit.

To find the power factor, you can use the power triangle, which shows the relationships between real power (P), reactive power (Q), and apparent power (S). The power factor is the cosine of the angle between the real power and the apparent power.

I hope this helps. Let me know if you have any further questions.