Hello,
I've already asked questions relative to a RL series circuit in another post, but somehow I'm no longer able to post on it. I'd like to thank the people who helped me: I managed to solve the problems and got the correct answers.
Unfortunately, I'm having a hard time again with another circuit, this time a RLC series-parallel.
I'm attaching the circuit sketch.
It's asking for:
a) Equivalent impedance of the circuit;
b) The instantaneous current and the RMS current in the circuit;
c) Phasor diagram for RMS V1, VA and VB;
d) Phasor diagram for RMS I1, I2 and I3;
e) The true, reactive and apparent powers used by the circuit.
a) I found the total impedance of the circuit by using the basic formulas, such as XL=wL and XC=1/(wC). By solving the circuit, I found it to be 667,52+j544,22 (ohm) or 861,25ohm with an phase angle of 39,19 degrees.
b) I'm really not sure if I got it right, but since the problem gave the maximum voltage on the source (169,7 volts), I simply divided it by the square root of two and found the RMS voltage to be approximately 120 volts.
To find the instantaneous current (max.) of the source, I applied Ohm's Law using the equivalent impedance and the max voltage. I found it to be I(t)=0.197sen(377t-0,684). The minus 0,684 is the phase angle of the current in radians. I'm not sure if its correct.
To find the RMS current, I divided the max. current magnitude(0,197) by the square root of two, and got I(rms)=0,139 with a phase angle of -39,19 degrees.
c,d) "Drawings". Since I'm not sure that I got the (b) values correctly, maybe they are wrong:
- I1=0,139A with an angle of -39,19 degrees;
- I2=0,33A with an angle of -70,51 degrees;
- I3=0,25A with an angle of approximately 90 degrees.
Since I1 are in series with the source, they are receiving all the RMS current sent by the source; to find I2, I found the voltage drop across the branch and its equivalent impedance. For I3, I simply used the voltage drop I found on the I2 branch, since they are in parallel.
e) Thats where I started to think I had messed up something. First, my apparent power, on its rectangular form, gave some crazy values. I got 12,92+j10,54 VA using the source voltage with 0 degrees multiplied by the conjugate complex of the current with -39,19 degrees.
Since it gave some pretty low value, I went with another method to try to find the apparent power. I got the individual power on each component. The true power component I calculated was 3355,6W, totally off from the 12,92 I found on the rectangular calculation. On the reactive power component, I subtracted the total capacitive reactive power from the total inductive power, and got 33,49 VAR. Using the pythagorean theorem, I found the apparent power to be 3355,77 VA. Thats still dumb. Since the phase difference between RMS voltage and RMS current is 39,19 degrees, which gives a power factor of 0,78 approximately, I can tell that there would be at least some intermediate contribution of the reactive power to the apparent power. By comparing the two power values, the reactive power is pretty much insignificant, which would lead to a much better power factor value, I think. I'm pretty sure I messed something along the way, and would appreciate some help.
I've already asked questions relative to a RL series circuit in another post, but somehow I'm no longer able to post on it. I'd like to thank the people who helped me: I managed to solve the problems and got the correct answers.
Unfortunately, I'm having a hard time again with another circuit, this time a RLC series-parallel.
I'm attaching the circuit sketch.
It's asking for:
a) Equivalent impedance of the circuit;
b) The instantaneous current and the RMS current in the circuit;
c) Phasor diagram for RMS V1, VA and VB;
d) Phasor diagram for RMS I1, I2 and I3;
e) The true, reactive and apparent powers used by the circuit.
a) I found the total impedance of the circuit by using the basic formulas, such as XL=wL and XC=1/(wC). By solving the circuit, I found it to be 667,52+j544,22 (ohm) or 861,25ohm with an phase angle of 39,19 degrees.
b) I'm really not sure if I got it right, but since the problem gave the maximum voltage on the source (169,7 volts), I simply divided it by the square root of two and found the RMS voltage to be approximately 120 volts.
To find the instantaneous current (max.) of the source, I applied Ohm's Law using the equivalent impedance and the max voltage. I found it to be I(t)=0.197sen(377t-0,684). The minus 0,684 is the phase angle of the current in radians. I'm not sure if its correct.
To find the RMS current, I divided the max. current magnitude(0,197) by the square root of two, and got I(rms)=0,139 with a phase angle of -39,19 degrees.
c,d) "Drawings". Since I'm not sure that I got the (b) values correctly, maybe they are wrong:
- I1=0,139A with an angle of -39,19 degrees;
- I2=0,33A with an angle of -70,51 degrees;
- I3=0,25A with an angle of approximately 90 degrees.
Since I1 are in series with the source, they are receiving all the RMS current sent by the source; to find I2, I found the voltage drop across the branch and its equivalent impedance. For I3, I simply used the voltage drop I found on the I2 branch, since they are in parallel.
e) Thats where I started to think I had messed up something. First, my apparent power, on its rectangular form, gave some crazy values. I got 12,92+j10,54 VA using the source voltage with 0 degrees multiplied by the conjugate complex of the current with -39,19 degrees.
Since it gave some pretty low value, I went with another method to try to find the apparent power. I got the individual power on each component. The true power component I calculated was 3355,6W, totally off from the 12,92 I found on the rectangular calculation. On the reactive power component, I subtracted the total capacitive reactive power from the total inductive power, and got 33,49 VAR. Using the pythagorean theorem, I found the apparent power to be 3355,77 VA. Thats still dumb. Since the phase difference between RMS voltage and RMS current is 39,19 degrees, which gives a power factor of 0,78 approximately, I can tell that there would be at least some intermediate contribution of the reactive power to the apparent power. By comparing the two power values, the reactive power is pretty much insignificant, which would lead to a much better power factor value, I think. I'm pretty sure I messed something along the way, and would appreciate some help.
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