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Fazza3_uae
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Determine the value of the inductance ...??
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.
Cos [tex]\phi[/tex] = XL / Z
Tan [tex]\phi[/tex] = XL - XC / R
w = 2*pi*f
Z2 = R2 + (XL - XC)2
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.
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.
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