# Theory question

Discuss Theory question in the Electrical Forum area at ElectriciansForums.net

M

#### macnab

Welcome to ElectriciansForums.net - The American Electrical Advice Forum

Hi guys, I'm studying electrical ac theory. My question is in regards to inductance and resistance. An inductor has a effective resistance of 4 ohms and a inductive reactance of 19.6. Total Z=20. Now in doing calculations for power etc the resistance is considered to be in series with the coil. At 60hz 120v the pf is 0.2 lagging and a phase angle of 78.5 degrees, thus the current is lagging by that amount. Now when using trigonometry the current in the pure resistance part of the series circuit is considered to be in phase with the voltage. However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current. So my question is how can the trigonometry state there is a current that is in phase with the voltage?

I did a plot of the vars supplied to the coil and vars returned to the supply, these are not equal, the vars supplied is higher. My point is that the true power in watts is the difference between the vars supplied and vars returned, not due to current that is "in phase" with the voltage - does this make sense or am I missing something.

Any thoughts really appreciated.

Mac.

#### bonjovi

##### -
Arms
bet you dont get many replies to this question lost me pal good luck

S

#### sripey

Hi guys, I'm studying electrical ac theory. My question is in regards to inductance and resistance. An inductor has a effective resistance of 4 ohms and a inductive reactance of 19.6. Total Z=20. Now in doing calculations for power etc the resistance is considered to be in series with the coil. At 60hz 120v the pf is 0.2 lagging and a phase angle of 78.5 degrees, thus the current is lagging by that amount. Now when using trigonometry the current in the pure resistance part of the series circuit is considered to be in phase with the voltage. However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current. So my question is how can the trigonometry state there is a current that is in phase with the voltage?

I did a plot of the vars supplied to the coil and vars returned to the supply, these are not equal, the vars supplied is higher. My point is that the true power in watts is the difference between the vars supplied and vars returned, not due to current that is "in phase" with the voltage - does this make sense or am I missing something.

Any thoughts really appreciated.

Mac.
What exactly are you trying to work out?

Inductive reactance is worked out as follows Xl=2piefl.

In an inductivive Cct current will always lag behind the voltage, depending on the amount of lag it may very well be in phase with the voltage.
As well as using trig to work this out you will need to be using "J" notation (other wise known as a complex number.

#### ian.settle1

##### -
Mentor
Arms
Hi guys, I'm studying electrical ac theory. My question is in regards to inductance and resistance. An inductor has a effective resistance of 4 ohms and a inductive reactance of 19.6. Total Z=20. Now in doing calculations for power etc the resistance is considered to be in series with the coil. At 60hz 120v the pf is 0.2 lagging and a phase angle of 78.5 degrees, thus the current is lagging by that amount. Now when using trigonometry the current in the pure resistance part of the series circuit is considered to be in phase with the voltage. However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current. So my question is how can the trigonometry state there is a current that is in phase with the voltage?

I did a plot of the vars supplied to the coil and vars returned to the supply, these are not equal, the vars supplied is higher. My point is that the true power in watts is the difference between the vars supplied and vars returned, not due to current that is "in phase" with the voltage - does this make sense or am I missing something.

Any thoughts really appreciated.

Mac.

Draw a phasor diagram

T

#### TPES

Ha ha, im also studdying AC theory at the minute, its a right Bas***d to learn.. well im finding it difficult anyway, Even i have no real idea what your question is..

P

#### pushrod

However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current.

Mac.
I would think there would only be the resultant current, which you might work out from a phasor diagram, but then i am probably the least experienced person on here K

#### Kirchoff1

The current I and Voltage V are in phase in a purely resistive circuit.
Power = VI (Apparent Power no Inductive Reactance)

But if Inductive Reactance (XL)
You need the Total Impedance Z ( sqrt(Rsquared + XL squared))
This now makes I=V/Z
The True Power = VI (I from your V/Z)
Also can be True Power = VI*Cos(angle)
Don't forget a low power factor means more current to meet the loads power requirements

#### bonjovi

##### -
Arms
****ed at the mo so leave it to better well strike that leave it to someone who has more tech knowledge in this field than me

R

#### RETIREDSPARKY

Current through R is in phase while current through L in lagging. The overall current is lagging V by 0.2. If you use trig to solve remember horizontal and vertical components.
The current in any inductive circuit will lag due to the magnetic field collapsing into the coil every quarter cycle and producing back emf.

G

#### Guest123

I would agree a phasor diagram seems to be the way to get an answer. Bear in mind your power factor of 0.2 though because as previously stated a higher current will be needed to operate the load.

M

Hi guys, I'm studying electrical ac theory. My question is in regards to inductance and resistance. An inductor has a effective resistance of 4 ohms and a inductive reactance of 19.6. Total Z=20. Now in doing calculations for power etc the resistance is considered to be in series with the coil. At 60hz 120v the pf is 0.2 lagging and a phase angle of 78.5 degrees, thus the current is lagging by that amount. Now when using trigonometry the current in the pure resistance part of the series circuit is considered to be in phase with the voltage. However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current. So my question is how can the trigonometry state there is a current that is in phase with the voltage?

I did a plot of the vars supplied to the coil and vars returned to the supply, these are not equal, the vars supplied is higher. My point is that the true power in watts is the difference between the vars supplied and vars returned, not due to current that is "in phase" with the voltage - does this make sense or am I missing something.

Any thoughts really appreciated.

Mac.

Hi there

sounds like you are forgetting the root (beer) mean sqaure value of .0707 based on the current value under the wave hence two currents thats the way i see it

anyone else see that one ??

P

#### PhaseShift

There isn't two currents, but two aspects of the same current operating at a "angle" to one another. Consider the case of a child's toy wagon. If you pull the handle, the result is the wagon moving horizontally. But if you look, you are also pulling the handle at an angle upward as well as horizontal. The resultant of the two forces is the force acting on the wagon. This is similar to how the resultant of the inductive reactance and resistance is the total impedance.

A

I think I see what you mean - pf through the resistor isn't unity, it's 0.2, same as through the rest of the cct.
Power factor is calculated using everything in the cct - the inductance in the coil causes the current to lag - the resistance doesn't make it lag any further, but at the same time it doesn't bring it closer to unity.

Am I making any sense?

W

#### WarrenG

There isn't two currents, but two aspects of the same current operating at a "angle" to one another. Consider the case of a child's toy wagon. If you pull the handle, the result is the wagon moving horizontally. But if you look, you are also pulling the handle at an angle upward as well as horizontal. The resultant of the two forces is the force acting on the wagon. This is similar to how the resultant of the inductive reactance and resistance is the total impedance.
Nice post - well put! V

#### Vinny

Hi guys, I'm studying electrical ac theory. My question is in regards to inductance and resistance. An inductor has a effective resistance of 4 ohms and a inductive reactance of 19.6. Total Z=20. Now in doing calculations for power etc the resistance is considered to be in series with the coil. At 60hz 120v the pf is 0.2 lagging and a phase angle of 78.5 degrees, thus the current is lagging by that amount. Now when using trigonometry the current in the pure resistance part of the series circuit is considered to be in phase with the voltage. However there iare not two currents in a series circuit, i.e. one in phase and the other lagging, there can be only one current, this being the lagging current. So my question is how can the trigonometry state there is a current that is in phase with the voltage?

I did a plot of the vars supplied to the coil and vars returned to the supply, these are not equal, the vars supplied is higher. My point is that the true power in watts is the difference between the vars supplied and vars returned, not due to current that is "in phase" with the voltage - does this make sense or am I missing something.

Any thoughts really appreciated.

Mac.
Your right there is only one current flowing and it will be lagging. But in order to discover by how much it’s lagging (the angle) you need to look at all the components of current in the cct individually. To do this you draw a phasor diagram which allows you to separate the currents into, in phase (resistive), leading (capacitive) and lagging (inductive) to see how each reactive and resistive element in the cct affects the resulting OVERALL supply current.
Changing the value of any one will lengthen or shorten its phasor line and hence change the lag/lead angle of the actual current flowing.
Hope Ive understood your question correctly and even more hope my answer’s correct

Reply to Theory question in the Electrical Forum area at ElectriciansForums.net