- #1

Fazza3_uae

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**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 V

_{max}leading V

_{C}. Answer in units of H.

## Homework Equations

Cos [tex]\phi[/tex] = X

_{L}/ Z

Tan [tex]\phi[/tex] = X

_{L}- X

_{C}/ R

w = 2*pi*f

Z

^{2}= R

^{2}+ (X

_{L}- X

_{C})

^{2}

## The Attempt at a Solution

First I used the 2

^{nd}Eq. Tan [tex]\phi[/tex] = X

_{L}- X

_{C}/ R

(R* Tan [tex]\phi[/tex])

^{2}= (X

_{L}- X

_{C})

^{2}

Then I used the 1

^{st}Eq. Cos [tex]\phi[/tex] = X

_{L}/ Z

Z

^{2}= R

^{2}+ (X

_{L}- X

_{C})

^{2}

I replaced (X

_{L}- X

_{C})

^{2}with (R* Tan [tex]\phi[/tex])

^{2}

then ,

Cos

^{2}[tex]\phi[/tex] = X

_{L}

^{2}/ (R

^{2}+ (X

_{L}- X

_{C})

^{2})

X

_{L}

^{2}= Cos

^{2}[tex]\phi[/tex] * (R

^{2}+ (X

_{L}- X

_{C})

^{2}) = w

^{2}L

^{2}

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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