RLC circuit -- determine the voltage across each element

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Discussion Overview

The discussion focuses on determining the voltage across each element in a series RLC circuit, including calculations for the resistor, inductor, and capacitor. Participants explore phasor representations and the implications of complex voltages.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant calculates the total impedance of the circuit and the total current, questioning if the voltage across the resistor can be found by multiplying the current by resistance.
  • Another participant confirms the method for calculating the voltage across the resistor and suggests that the sum of the voltages should equal the source voltage.
  • Further calculations for the voltages across the capacitor and inductor are presented, with a participant noting that the sum of these voltages does not equal the source voltage.
  • Participants discuss the importance of considering angles in voltage calculations and suggest using complex values for accurate results.
  • One participant provides the calculated voltages in phasor form for the resistor, inductor, and capacitor, and attempts to sum them to find the total voltage.
  • Another participant advises maintaining precision in intermediate calculations to avoid rounding errors.
  • A question is raised about the total impedance if the components were in parallel, leading to confirmation from another participant.

Areas of Agreement / Disagreement

Participants generally agree on the methods for calculating voltages across the circuit elements, but there is uncertainty regarding the sum of these voltages equating to the source voltage. The discussion remains unresolved regarding the implications of this discrepancy.

Contextual Notes

Participants express uncertainty about the correct approach to summing complex voltages and the impact of phase angles on these calculations. There is also a lack of consensus on the implications of the total impedance when components are arranged in parallel.

TheRedDevil18
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Homework Statement


For the series RLC circuit shown in Fig. Q8, determine the voltage across each element, and draw a complete phasor diagram.

os69eg.jpg


Homework Equations

The Attempt at a Solution



Total Impedance:
Z = R+Xc+Xl
= 75 - 60j + 25j
= 75-j35

Z = 82.76∠-25.02 (Phasor form)

Total Current:
I = V/Z
= (10∠0)/(82.76∠-25.02)
= 0.12∠25.02

Now my question is when finding the voltage across the resistor will it just be the magnitude of the current*resistance ie, 0.12*75 ?

Also when finding the voltage across the inductor, is this correct ?
V = (0.12∠25.02)*(75.06∠18.43)......Z = 75+j25, in phasor form = 75.06∠18.43
= 9∠43.45

And the capacitor
V = (0.12∠25.02)*(96.05∠-38.66)......Z = 75-j60, in phasor form = 96.05∠-38.66
= 11.53∠-13.64

Thanks
 
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TheRedDevil18 said:
Now my question is when finding the voltage across the resistor will it just be the magnitude of the current*resistance ie, 0.12*75 ?
Sure.

If you add all values you should get the 10 V of the source back. Does that happen?
 
mfb said:
Sure.

If you add all values you should get the 10 V of the source back. Does that happen?

Okay, so the voltage across the resistor would be V = 0.12*75 = 9V

For the voltage across the capacitor, it should be
V = I*Z
= (0.12∠25.02)*(60∠-90)
= 7.2∠-64.98

Voltage across the inductor
V = I*Z
= (0.12∠25.02)*(25∠90)
= 3∠115.02

But 9+7.2+3 does not equal the voltage of the source ?
 
You have to take the angles into account. Or calculate the real and imaginary part separately.
 
TheRedDevil18 said:
Okay, so the voltage across the resistor would be V = 0.12*75 = 9V
That will give you the magnitude of the voltage across the resistor, but won't give you the phase of that voltage. Use the complex current for the calculation.
For the voltage across the capacitor, it should be
V = I*Z
= (0.12∠25.02)*(60∠-90)
= 7.2∠-64.98

Voltage across the inductor
V = I*Z
= (0.12∠25.02)*(25∠90)
= 3∠115.02

But 9+7.2+3 does not equal the voltage of the source ?
The voltages are all complex values. Add appropriately.
 
Okay,

Voltage of resistor
Vr = 9∠25.02

Voltage of inductor
Vl = 3∠115.02

Voltage of capacitor
Vc = 7.2∠-64.98

So, Vt = Vr+Vl+Vc
= 3.05-6.52j-1.27+2.72j+8.16+3.81j
Vt = 9.94+0.01j

|Vt| = 9.94V
 
Looks good.

Keep a few extra digits in intermediate values in order to prevent truncation and roundoff errors from creeping into final values. Round results for presentation to the required sig figs after you're done calculating.
 
Ok, thanks guys

One last question, if they where all in parallel then the total impedance would be,
1/Z = 1/R + 1/Xc + 1/Xl ?
 
TheRedDevil18 said:
Ok, thanks guys

One last question, if they where all in parallel then the total impedance would be,
1/Z = 1/R + 1/Xc + 1/Xl ?
Yes.
 

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