Solving Series Circuit with 10Ω Resistor, Coil and Capacitor

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Discussion Overview

The discussion revolves around solving a series circuit problem involving a 10Ω resistor, a coil, and an ideal capacitor connected to a 200 V, 60 Hz power supply. Participants explore the calculations for voltage across the capacitor and the resultant voltage across the resistor and coil, engaging in both technical reasoning and conceptual clarification.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster calculates the voltage across the resistor and attempts to find the voltage across the capacitor using phasor diagrams and cosine law.
  • Some participants question the assumptions made about the circuit components, particularly the power factor and the implications of the coil being described as a coil rather than an ideal inductor.
  • One participant suggests that the coil likely has resistance, which could affect the voltage calculations, and proposes that the power factor indicates this resistance.
  • Another participant emphasizes the need for a correct phasor diagram, indicating that it should represent the voltages across the resistor, coil, and capacitor appropriately.
  • There is a suggestion that the calculations should begin with determining the resistance of the coil and its inductive reactance before proceeding with the main calculations.
  • Some participants express uncertainty about the correctness of their answers and seek confirmation or solutions from others.
  • A later reply asserts that the original poster's answers are incorrect and suggests a specific value for the capacitor size as a check.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the original poster's calculations. Multiple competing views regarding the assumptions about the coil's resistance and the implications for the circuit analysis remain unresolved.

Contextual Notes

Participants highlight potential limitations in the original poster's assumptions about the circuit components, particularly regarding the coil's resistance and the interpretation of the power factor. The discussion also reflects uncertainty about the correct approach to the calculations and the interpretation of the phasor diagram.

pishkil
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Homework Statement



A series circuit consisting of a 10 ohm resistor, a coil and an ideal capacitor is connected across a 200 V, 60 Hz power supply. The current drawn is 8 A. The voltage across the coil is 120 V and its power factor is 0.8 lagging. Determine (a) the voltage across the capacitor, and (b) the resultant voltage across the resistor and the coil.

Homework Equations



V = I*Z; V(resistor) = I*R
Phasor angle(coil) = PHI = cos^-1(0.8); wherein ^-1 indicates inverse.

The Attempt at a Solution



Solving first V(resistor):

V(resistor) = I*R
" = 8 A(10 ohms)
V(resistor) = 80 V

Phasor angle(coil) = PHI = cos^-1(0.8)
Phasor angle(coil) = PHI = 36.87 degrees

Here's the phasor diagram:

https://www.physicsforums.com/attachment.php?attachmentid=42443&stc=1&d=1325682519

By using cosine law to solve for V(RL):

V(RL)^2 = V(resistor)^2 + V(coil)^2 - 2V(resistor)V(coil)cos(180 - PHI)
V(RL)^2 = 80^2 + 120^2 - 2(80)(120)cos(180 - 36.87)
V(RL) = 190.16 V => (b)

Now solving for THETA(the phasor angle of V(RL)) by using sine law:

sin(THETA)/V(coil) = sin(180 - PHI)/V(RL)

Solving for THETA:

THETA = 22.25 degrees

Then by using vector component method in order to solve for V(capacitor) and the ideal capacitor's capacitance:

x-comp y-comp

V(RL) 190.16cos(22.25) 190.16sin(22.25)
V(C) V(C)*cos(-90) V(C)*sin(-90)

V(source) 200cos(BETA) 200sin(BETA)

Using summation of x-comp to solve for angle BETA:

190.16cos(22.25) + V(C)*cos(-90) = 200cos(BETA)
BETA = 28.36 degrees (must be negative since BETA's value must be always between the value of THETA and -90 degrees)

Using summation of y-comp to now solve for V(C):

190.16sin(22.25) + V(C)*sin(-90) = 200sin(-28.36)
V(C) = 167.01 V => (a)

So am I doing the right thing? If not, please show your solution. Thanks!
 

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I am uncertain about the components in your circuit!
If the supply voltage is 200V and the power factor is 0.8 then the voltage across the resistance should be VsCos∅ = 200 x 0.8 = 160V
But the current is given as 8A and the resistance as 10Ω which means a voltage of 80V across the resistance. Does the coil have resistance itself?
 
Last edited:
Also... your phasor diagram should have only 3 arrows
A vertical (+y direction) to represent Vl
A vertical (-y direction) to represent Vc and
A horizontal (+ x direction) to represent Vr (this would be total R which makes me think your coil has a resistance other than the 10Ω stated in the question.
Hope this helps you
 
technician said:
Also... your phasor diagram should have only 3 arrows
A vertical (+y direction) to represent Vl
A vertical (-y direction) to represent Vc and
A horizontal (+ x direction) to represent Vr (this would be total R which makes me think your coil has a resistance other than the 10Ω stated in the question.
Hope this helps you

The problem statement is a bit sneaky. It states that there is a coil rather than an inductor, and then says that there is an ideal capacitor. From that I think we should gather that the while the capacitor is ideal the coil is not; it will have some resistance. This is backed up by the statement assigning a power factor to the coil. The coil inductance and resistance can be calculated from the given information.
 
The coil does have some resistance and so it is useful to do that part of the calculation first and then put the values obtained into a main calculation.

This diagram might explain the process:

http://dl.dropbox.com/u/4222062/series%20cct%205jan.PNG
 
Last edited by a moderator:
that makes more sense ! I got sensible answers.
Does anyone know the correct answers?
 
technician said:
that makes more sense ! I got sensible answers.
Does anyone know the correct answers?

I have solutions, but I wonder about giving them before the OP works them out?

Could I send them to you via PM?
 
@vk6kro, are my answers incorrect? if so, could you please show to us the final answers? i am also in doubt of my answers.
 
No, your answers are not corrent.

Did you understand the diagrams I posted above?
First you need to work out the size of the resistance of the coil and the inductive reactance of the coil.

Then you should put those values into the main part of the problem.

The diagrams actually show you how to do it. Try to follow a logical procedure and you should get it.

As a check, you should get 132 uF for the capacitor size.
 

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