How Do You Calculate Resistance and Inductance in a Single Phase A.C. Coil?

  • Thread starter Thread starter Physicist3
  • Start date Start date
  • Tags Tags
    Coil Phase
Click For Summary

Discussion Overview

The discussion revolves around calculating the resistance and inductance of a single-phase A.C. coil connected to a 230V 50Hz supply, given a current of 10A at a phase angle of 30 degrees. Participants explore the application of electrical principles and formulas to derive these values.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant attempts to calculate resistance using the formula R=V/I, arriving at a value of 16.26Ω, but notes a discrepancy with a book answer of 21.65Ω.
  • The same participant calculates inductance using the formula XL=2∏fL, obtaining 0.052H, while the book states 39.8mH, leading to confusion about the calculations.
  • Another participant suggests modeling the circuit as a series circuit of R and L, indicating that the current is 10A and that the parameters are already in RMS, implying no further conversion is needed.
  • Some participants express difficulty in determining how to find the voltage across each element given the source voltage, frequency, and current.
  • There is a suggestion to use a right-angled triangle to visualize how the voltage across R and L contributes to the total voltage of 230V, utilizing the known power-factor angle.
  • Further clarification is provided regarding the phase relationship of voltages across R and L, noting that the voltage across R is in phase with the current while the voltage across L leads the current by 90 degrees.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and confusion regarding the calculations, with no consensus reached on the correct values for resistance and inductance. Multiple approaches and interpretations are presented without resolution.

Contextual Notes

Some participants highlight the need for clarity on how to apply trigonometric relationships to the voltages across the components, indicating potential gaps in assumptions or steps in the calculations.

Physicist3
Messages
103
Reaction score
0
1. A coil connected to a 230V 50Hz supply takes a current of 10A at a phase angle of 30o Calculate the resistance and inductance of the coil



2. i = ImSinωt, R=V/I and XL=2∏fL



3. To get the resistance I used the value of 10A to get the value of Imby dividing 10 by sin30 which = 20A. I then multiplied this by 0.707 to get RMS value as I believe the Voltage to be RMS as well. I then divided voltage by current to get resistance of 16.26Ω but the answer in the book says 21.65Ω and I can't seem to get this value. For the inductance I divided voltage by current again to get XL which I get as 16.26 again. I then divided this by 2∏ x 50 to get a value of 0.052H but the book says 39.8mH and I can't seem to work out how to get to the answers in the book
 
Last edited by a moderator:
Physics news on Phys.org
Model it by a series circuit: R and L. Of the 230V applied, use trig to determine how much voltage appears across the R and how much across Ѡ.L

You know the current in each series element is 10A.

Parameters are already in RMS, so no further conversion is needed.
 
Sorry but am I missing something because I am really struggling as how to find how much voltage is in each element if I've been given a source voltage, frequency and current?
 
Physicist3 said:
Sorry but am I missing something because I am really struggling as how to find how much voltage is in each element if I've been given a source voltage, frequency and current?

You are also told the power-factor angle, so ...

You draw a right-angled triangle showing how the voltage across R adds to the voltage across L to produce 230V. Mark in the angle whose value you know.
 
Explaining further: because the elements are in series, it is convenient that we take the current as reference, because that current is common to each element (it's identical in each element at all times). The voltage across the R is in phase with this current, (it always is for a resistor) so you can draw the voltage phasor as being parallel to the current phasor. The voltage across the L is 90 degrees ahead of the current, so you can draw the inductor's voltage phasor as 90 degrees ahead of the current.
 

Similar threads

Engineering How to calculate rotor flux of the three phase squirrel cage induction motor?
  • · Replies 4 ·
Replies
4
Views
3K
Coil and resistor in parallel -- How to calculate the phase angle?
  • · Replies 4 ·
Replies
4
Views
3K
Calculating Resistance and Inductance of Coil in AC Circuit
  • · Replies 3 ·
Replies
3
Views
8K
Single Phase Controlled Rectifier Problem
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Mutual inductance in a transformer
  • · Replies 16 ·
Replies
16
Views
5K
Undergrad How induction works within a coil (nuances of it)
  • · Replies 6 ·
Replies
6
Views
2K
Calculating Complex Apparent Power in a Sinusoidal Circuit
  • · Replies 12 ·
Replies
12
Views
2K
Average current in single phase bridge converter SCR
  • · Replies 3 ·
Replies
3
Views
19K
Engineering Ac circuit non inductive resistor and a coil
  • · Replies 1 ·
Replies
1
Views
5K
Average battery current in battery charger
  • · Replies 7 ·
Replies
7
Views
1K