Circuito RLC

[Carlos]

Referencias:
Wikipedia: RLC circuit


Frecuencias e impedancias:

[tex]\omega= rad/s[/tex]

[tex]f= Hz[/tex]

[tex]\omega_0=2 \pi f[/tex]


[tex]Z_L=\omega_0\cdot L[/tex]

[tex]Z_C=\dfrac{1}{\omega_0\cdot C}[/tex]


Frecuencia de resonancia e impedancia de resonancia:

[tex]\omega_0 =\dfrac {1}{\sqrt{L\cdot C}}[/tex]

[tex]Z_0 =\sqrt{\dfrac {L}{C}}[/tex]

[tex]L =\dfrac {1}{C\cdot \omega_0^{2}}[/tex]

[tex]C =\dfrac {1}{L\cdot \omega_0^{2}}[/tex]


Factor de calidad Q:

[tex]Q = \dfrac{Z_0}{R} = \dfrac{1}{R} \sqrt{\dfrac {L}{C}}[/tex]


Frecuencia de resonancia con resistencia:

[tex]\omega_d = \omega_o \sqrt{1 - \dfrac{1}{4Q^{2}}}[/tex]

[tex]Q=1 \to \omega_d = 0,866\cdot \omega_0[/tex]
[tex]Q=2 \to \omega_d = 0,968\cdot \omega_0[/tex]
[tex]Q=5 \to \omega_d = 0,995\cdot \omega_0[/tex]