# Determine the value of the inductance ?

1. Dec 21, 2009

### Fazza3_uae

Determine the value of the inductance ...??

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

3. The attempt at a solution

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

(R* Tan $$\phi$$)2 = (XL - XC)2

Then I used the 1st Eq. Cos $$\phi$$ = XL / Z

Z2 = R2 + (XL - XC)2

I replaced (XL - XC)2 with (R* Tan $$\phi$$)2

then ,

Cos2 $$\phi$$ = XL2 / (R2 + (XL - XC)2)

XL2 = Cos2 $$\phi$$ * (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: Dec 21, 2009
2. Dec 21, 2009

### rl.bhat

Re: Determine the value of the inductance ...??

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. Dec 24, 2009

### Fazza3_uae

Re: Determine the value of the inductance ...??

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. Dec 24, 2009

### rl.bhat

Re: Determine the value of the inductance ...??

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. Dec 24, 2009

### Fazza3_uae

Re: Determine the value of the inductance ...??

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 ..

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 ...