Determine the value of the inductance ?

In summary, to determine the value of the inductance in a series RLC circuit, where the voltage across the capacitor is out of phase with the applied voltage by 54 degrees with Vmax leading VC, the equation tan(theta) = R/(XL - XC) can be used. The voltage across the capacitor will be greater than the voltage across the inductor, and the voltage across the inductor will lead the voltage across the capacitor.
  • #1
Fazza3_uae
51
0
Determine the value of the inductance ...??

Homework Statement




Consider a series RLC circuit. The applied voltage has a maximum value of 210 V and oscillates at a frequency of 76 Hz. The circuit contains an inductor whose inductance can be varied, a 900 ohm resistor, and a 1 μF capacitor.Determine the value of the inductance such that the voltage across the capacitor is out of phase with the applied voltage by 54◦, with Vmax leading VC. Answer in units of H.

Homework Equations



Cos [tex]\phi[/tex] = XL / Z
Tan [tex]\phi[/tex] = XL - XC / R
w = 2*pi*f
Z2 = R2 + (XL - XC)2



The Attempt at a Solution



First I used the 2nd Eq. Tan [tex]\phi[/tex] = XL - XC / R

(R* Tan [tex]\phi[/tex])2 = (XL - XC)2

Then I used the 1st Eq. Cos [tex]\phi[/tex] = XL / Z

Z2 = R2 + (XL - XC)2

I replaced (XL - XC)2 with (R* Tan [tex]\phi[/tex])2

then ,

Cos2 [tex]\phi[/tex] = XL2 / (R2 + (XL - XC)2)

XL2 = Cos2 [tex]\phi[/tex] * (R2 + (XL - XC)2) = w2L2

Then , L = 1.8827 H which is wrong .

Am i in the right direction , if not please point me towards it . Thanks.
 
Last edited:
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  • #2


Since the voltage across the capacitor is out of phase with the applied voltage, angle between Vc and hence VC - VL and Vmax is 54 degrees.
So tan(54) = R/(XC - XL)
Solve for XL and find L.
 
  • #3


wow ..thx a ton rl.bhat.

whould u tell what expression must i use if the question says the voltage across the inductor ??

and how did you get Vc-Vl why it not Vl-Vc ??

thanks again ..
 
  • #4


Since applied voltage leads with Vc, Vc must be greater than VL. So net voltage across reactance should be VC - VL.
If VL leads with the applied voltage then you have to take VL - VC.
 
  • #5
Thanks again for the clarification.

Hmmmm... why tan(theta) why not cos(theta) ...??

You have answered same question before and i want to understand it 2 ..

https://www.physicsforums.com/showthread.php?t=328964


check the link .

If i was answering the question i would say the answer must be in this form ...

tan(theta)= R / XL-XC

Because it says that Vl is leading so it is greater that Vc like what you 've said ...

But you answered cos(theta)=Xc/Z ,,,,,??
 
  • #6


In both the treads VC is out of phase with the applied voltage.
So you can write either tanθ = R/(XC - XL) or cosθ = (XC - XL)/Z. In the second thread it was typo.
In LCR circuit always Vmax leads VC and VL leads Vmax. So it does not change expression for tanθ. In your relevant equation the angle φ is the phase difference between the current and Vmax.
 

Related to Determine the value of the inductance ?

1. How is inductance measured?

Inductance is measured in units called Henrys (H) using a device called an inductance meter.

2. What factors affect the value of inductance?

The value of inductance is affected by the number of turns in the coil, the size and shape of the coil, and the material used for the core (if present).

3. How does inductance affect electrical circuits?

Inductance affects electrical circuits by resisting changes in current flowing through them, causing a delay in the current response. It also stores energy in the form of a magnetic field.

4. Can the value of inductance be changed?

Yes, the value of inductance can be changed by altering the physical characteristics of the coil, such as the number of turns, the size, or the material used for the core.

5. How is inductance used in practical applications?

Inductance is used in many practical applications, such as in electronic filters, transformers, and motors. It is also a crucial component in circuits that generate and transmit radio signals.

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