Hi, Can anyone please help with the attached question. Im unsure as of how to calculate the inductance and show the working. Any help would be appreciated. Thanks!

 

How do you model the coil? Obviously, as a resistor with an inductor; but are they in series or in parallel? If you were given an RL network, could you calculate the current through it? So if you are given the current but not the value of L then do the calculation in reverse.

 

Hi RBR1317, Thanks for your help.

Its a series circuit. I'm struggling to work out XL so I can do the formula: L= XL/2pi x F

 

Q3 (a)
When the coil is connected to the 100V DC behave purely resistive -> Use Ohm's Law:
R=U/I=100V/12.5A=8ohm

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/imped.html
In AC we have impedance instead of resistance.

We know that the coil make a phase shift 90 degrees voltage-current.
Resistor make no phase shift between voltage electric current.

We have right-angled triangle where the two catheters are impedances(for L and R), hypotenuse is results impedance.

I=U/Z => Z=U/I=100V/5A=20V/A (It does not specify what voltage is. It could be multiplied by the square root of 2)

Applying Pythagoras' theorem:
Z*Z=R*R+XL*XL
Without measurement units:
20*20=8*8+XL*XL =>XL*XL=345 =>XL=18.3 (ohm)

XL=2*PI*frequency*L

18.3=2*3.14*50*L => L=0.0586H=58.6mH

(b) for 200V 100Hz

XL=2*PI*frequency*L=18.3*2=36.6(ohm)

Z*Z=8*8+36.6*36.6 => Z=37.46 (ohm)

I=U/Z=200V/37.46ohm=5.33A

 

Q3 (b)(c)
reduce the current to 4A:

I=U/Z=200V/Z=4A =>Z=200V/4A=50ohm

Adding additional resistance R1:
Z*Z=(8+R1)*(8+R1)+36.6*36.6
50*50=(8+R1)*(8+R1)+36.6*36.6 =>
(8+R1)*(8+R1)=1160.5 =>
(8+R1)=34.06 =>
R1=26.06 (I made calculations approximate)

(b)

In fact these hiding following differential equation::
L*di/dt+i*R=u(t); i=i(t)

 

real power/apparent power=resistor power/ power apparent for the whole circuit.
Only one resistor is dissipating heat (power).
P=U*I=I*I*R
Pr/Pa=I*I*R/I*I*Z (Attention that here not sure!!!!!!!!)

The series circuit current intensity is the same so it simplifies:
Pr/Pa=R/Z=8/37.46=0,213561131874

 

Brilliant Motanache,

Thanks very much for all of your help, much appreciated!!