AC and DC supplied coils

tesseract77 · May 13, 2022

Hi All,

I am currently learning about AC and DC supplied coil and have been given the scenario below. I understand the first few steps but then I am unsure of how to proceed from step 3 onwards. I am very new to this so any help is much appreciated.

1. A coil is connected to a 100V DC supply and the current is of 10A. Calculate the resistance (R) of the coil.
- I Calculate this to be 10 Ohms.

2. The same coil is connected to 100V AC. Why is the current found to be 6A? Provide an explanation of why the a.c current is lower.
- When DC current flows into the coil it only offers resistance based the number of turns(N) diameter of coil (D) diameter of the wire (d) and material of the wire having resistivity (r). Whereas In AC the coils offers not only resistance but also inductive reactance. X equal to 2πFL where f is frequency of AC and L is inductance of the coil. The total impedance of coil in AC is square root of the sum of R square and X squared. The impedance is greater than R. Therefore in AC the coil draws less current.

3. If the supply voltage is 100V A.C with a period of 20ms, and the supply current (is) taken by the coil is 6A, calculate the frequency of the supply, overall impedance, inductive reactance and the inductance of the coil.
-Frequency of the supply = 50Hz
- I am unsure of how to calculate the overall impedance, inductive reactance and inductance of the coil.

4.Calculate the power factor and phase angle of the coil. (Check angle against your triangle)

5.Sketch a waveform of the voltage/current values calculated, over two complete cycles and use this to explain why the current of an R-L circuit is said to be 'out of phase' by the angle calculated.

6. Explain the relationships between voltage/current phase shifts for an R-L circuit and for an R-C circuit.

7. A capacitor is to be connected in parallel with the coil. If the capacitive reactance has the same value, in ohms, as the inductive reactance calculated above, calculate the value of capacitor required.

8. If a capacitor of a higher value is connected instead of the size calculated above, explain what would happen to the voltage/current phase relationship.

9. If the supply frequency was increased to 10^3 Hz. What would the new reactance of the capacitor from (7) above be.

TIA

Julie. · May 14, 2022

tesseract77 said:
Hi All,

I am currently learning about AC and DC supplied coil and have been given the scenario below. I understand the first few steps but then I am unsure of how to proceed from step 3 onwards. I am very new to this so any help is much appreciated.

1. A coil is connected to a 100V DC supply and the current is of 10A. Calculate the resistance (R) of the coil.
- I Calculate this to be 10 Ohms.

2. The same coil is connected to 100V AC. Why is the current found to be 6A? Provide an explanation of why the a.c current is lower.
- When DC current flows into the coil it only offers resistance based the number of turns(N) diameter of coil (D) diameter of the wire (d) and material of the wire having resistivity (r). Whereas In AC the coils offers not only resistance but also inductive reactance. X equal to 2πFL where f is frequency of AC and L is inductance of the coil. The total impedance of coil in AC is square root of the sum of R square and X squared. The impedance is greater than R. Therefore in AC the coil draws less current.

3. If the supply voltage is 100V A.C with a period of 20ms, and the supply current (is) taken by the coil is 6A, calculate the frequency of the supply, overall impedance, inductive reactance and the inductance of the coil.
-Frequency of the supply = 50Hz
- I am unsure of how to calculate the overall impedance, inductive reactance and inductance of the coil.

4.Calculate the power factor and phase angle of the coil. (Check angle against your triangle)

5.Sketch a waveform of the voltage/current values calculated, over two complete cycles and use this to explain why the current of an R-L circuit is said to be 'out of phase' by the angle calculated.

6. Explain the relationships between voltage/current phase shifts for an R-L circuit and for an R-C circuit.

7. A capacitor is to be connected in parallel with the coil. If the capacitive reactance has the same value, in ohms, as the inductive reactance calculated above, calculate the value of capacitor required.

8. If a capacitor of a higher value is connected instead of the size calculated above, explain what would happen to the voltage/current phase relationship.

9. If the supply frequency was increased to 10^3 Hz. What would the new reactance of the capacitor from (7) above be.

TIA

1. A coil is connected to a 100V DC supply and the current is of 10A. Calculate the resistance (R) of the coil.
- I Calculate this to be 10 Ohms.

Correct

2. The same coil is connected to 100V AC. Why is the current found to be 6A? Provide an explanation of why the a.c current is lower.
- When DC current flows into the coil it only offers resistance based the number of turns(N) diameter of coil (D) diameter of the wire (d) and material of the wire having resistivity (r). Whereas In AC the coils offers not only resistance but also inductive reactance. X equal to 2πFL where f is frequency of AC and L is inductance of the coil. The total impedance of coil in AC is square root of the sum of R square and X squared. The impedance is greater than R. Therefore in AC the coil draws less current.

Correct(ish), though to be picky the frequency is f not F in your equation, F is farad which is a measure of capacitance not frequency - this could/should lose you points in marking.

3. If the supply voltage is 100V A.C with a period of 20ms, and the supply current (is) taken by the coil is 6A, calculate the frequency of the supply, overall impedance, inductive reactance and the inductance of the coil.
-Frequency of the supply = 50Hz

Correct

- I am unsure of how to calculate the overall impedance, inductive reactance and inductance of the coil.

You have basically answered this above

Z = V/I but using the 100V and 6A rather than 10A - this is overall impedance

you said Z^2 = R^2 + X^2

so just work backwards X^2 = Z^2 - R^2

You have Z and R from earlier calculations, so this would give you inductive reactance.

You said X(l) = 2πfL so work backwards again - rearrange for L and use the X, and f you have now calculated to calculate L.

4.Calculate the power factor and phase angle of the coil. (Check angle against your triangle)

You have a triangle formed by Z, X, & R.

X and R are at right angles and Z is the Hypotenuse

You can draw this, then look at the angles, calculate them (using SOH, CAH etc - sin, cos) thus you can calculate the phase angle, and hence power factor

5.Sketch a waveform of the voltage/current values calculated, over two complete cycles and use this to explain why the current of an R-L circuit is said to be 'out of phase' by the angle calculated.

So draw a couple of cycles of ac sine wave to represent the voltage, then superimpose a couple of cycles of sine wave to represent the current, however this would be displaced by the phase angle you calculated above - will it lead (in advance) of the voltage or will it lag (behind) ? - refer to your notes.

6. Explain the relationships between voltage/current phase shifts for an R-L circuit and for an R-C circuit.

Having referred to your notes, for 5. Above you should be able to answer this.

7. A capacitor is to be connected in parallel with the coil. If the capacitive reactance has the same value, in ohms, as the inductive reactance calculated above, calculate the value of capacitor required.

So this is saying X(c) = X(l) as you calculated X(l) above you now know X(c)

You had a formula for X(l) which you got from your notes, now you should be able to find a similar one for capacitance.

Rearrange this formula to give C as you have X, and f and calculate C

8. If a capacitor of a higher value is connected instead of the size calculated above, explain what would happen to the voltage/current phase relationship.

Think about this, perhaps try some numbers and calculate what the new total Z is and whether it looks overall more like a capacitance or more like an inductance.

What would that do to the phase angle?

9. If the supply frequency was increased to 10^3 Hz. What would the new reactance of the capacitor from (7) above be.

As you have found the formula for X(c) above, recalculate using C as already determined, but the new value for f