Engineering Calculating values of impedance in a series/parallel circuit

[Rougarou22]

Homework Statement

Hello everyone, I have recently come under some stress from not being able to get these answers correct. I need to calculate these values:

1. Zeq
2. IT
3. XL2
4. XL1
5. VR1
6. VR2
7. VL1
8. VL2

For this series circuit:

And these values:

1. Zeq
2. IT
3. XL2
4. XL1
5. IR1
6. IR2
7. IL1
8. IL2

For this parallel circuit:

Homework Equations

I have been using these equations, but I am told that they are incorrect. My professor will not indicate what the correct equations are and I cannot find them in my textbook or online. Any help would be appreciated.

Zeq = sqrt(RT^2+XL^2) where XL is both values of XL1 and XL2 added together.
IT = Vs/ZT This is where I get confused, is ZT the same as Zeq?
XL2 = (2*pi*Frequency*L2)
XL1 = (2*pi*Frequency*L1)
VR1 = (R1/RT)*Vs
VR2 = (R2/RT)*Vs
VL1 = (L1/LT)*Vs Where LT is L1 and L2 added together.
VL2= (L2/LT)*Vs
IR1= I could not find the equation for this value.
IR2 = I could not find the equation for this value.
IL1 = Vs/L1
IL2 = Vs/L2

The Attempt at a Solution

Here are the values that I came up with for the series circuit:

Phase = -tan((942.48+502.65)/100) = 86.04 degrees.
a. Zeq = 15Vrms / .03333A = 450ohms
b, It = 15Vrms/450ohms = 33.33mA∠-86.04 degrees
c. XL1 = (2*pi*1000Hz*.150H) = 942.48ohms
d. XL2 = (2*pi*1000Hz*.08) = 502.65ohms
e. VR1 = 150ohms/450ohms * 15Vrms = 5Vrms ∠0 degrees
f. VR2 = 300ohms/450ohms * 15Vrms = 10Vrms ∠0 degrees
g. VL1 = .08H/.23H * 15Vrms = 5.22Vrms ∠-90 degrees
h. VL2 = .150/.23H * 15Vrms = 9.78Vrms ∠-90 degrees And here are the values I came up with for the parallel circuit: a. Zeq = 15Vrms / .03333 = 450ohms
b. IT = 33.33mA ∠-86.04 degrees
c. XL2 = (2*pi*1000Hz*.150H) = 942.48ohms
d. XL1 = (2*pi*1000Hz*.08H) = 502.65ohms
e. VR1 = 150ohms/450ohms * 15Vrms = 5Vrms ∠0 degrees
f. VR2 = 300ohms/450ohms * 15Vrms = 10Vrms ∠0 degrees
g. IL1 = 15Vrms/.08H = 187.5A.
h. IL2 = 15Vrms/.150H = 100A

Any help at all would be very, very much appreciated. I really cannot find the equations for the life of me, and it is frustrating.

 

[Hesch]

Zeq = sqrt(RT^2+XL^2) where XL is both values of XL1 and XL2 added together.

That's correct as for the absolute value of Z_eq, ( | Z_eq | ).

Are you not familiar with complex impedances ? Here is the value:

Z_eq = ( R1+R2 ) + jω( L1+L2 )

You can calculate exactly like if all the impedances were ohmic, just using complex values instead of real values.

It will be much more easy ( your calculator will do the job ) to calculate voltages, current, phases, etc. using complex values:

As for the series connection, IR1 = IR2 = IL1 = IL2 = V_s / Z_eq ( like I = V / R ).

 

[Rougarou22]

That's correct as for the absolute value of Z_eq, ( | Z_eq | ).

Are you not familiar with complex impedances ? Here is the value:

Z_eq = ( R1+R2 ) + jω( L1+L2 )

You can calculate exactly like if all the impedances were ohmic, just using complex values instead of real values.

It will be much more easy ( your calculator will do the job ) to calculate voltages, current, phases, etc. using complex values:

As for the series connection, IR1 = IR2 = IL1 = IL2 = V_s / Z_eq ( like I = V / R ).

Thank you very much for the reply! I am not familiar with complex impedances. In Zeq = (R1+R2) + jω(L1+L2), what values are "j" and "ω"? So IR1, IR2, IL1 and IL2 are all calculated by Vs/Zeq?

 

[Hesch]

what values are "j" and "ω

j ( also called "i" ) is the imaginary operator: j² = -1.
ω is the angular velocity in radians/sek. ( ω = 2πf ).

IR2, IL1 and IL2 are all calculated by Vs/Zeq?

Yes, through all components in series, the currents are identical ( Kirchhoffs 1. law, KCL ).

I'm sorry, I thought that the complex values of impedances was what your professor meant. But you will learn about these complex impedances. I promise.

 

[Rougarou22]

j ( also called "i" ) is the imaginary operator: j² = -1.
ω is the angular velocity in radians/sek. ( ω = 2πf ).

Yes, through all components in series, the currents are identical ( Kirchhoffs 1. law, KCL ).

I'm sorry, I thought that the complex values of impedances was what your professor meant. But you will learn about these complex impedances. I promise.

Alright, everything makes much more sense now. Thank you very much for your help, I truly appreciate it!