Answer: [tex]71.16\ Hz[/tex]
Explanation:
Given
Capacitance [tex]C=100\ \mu F[/tex]
Resistance [tex]R=500\ \Omega[/tex]
Inductance [tex]L=50\ mH[/tex]
In LCR circuit, current is maximum at resonance frequency i.e.
[tex]X_L=X_C\ \text{and}\ \omega_o=\dfrac{1}{\sqrt{LC}}[/tex]
Insert the values
[tex]\Rightarrow \omega_o=\dfrac{1}{\sqrt{50\times 10^{-3}\times 100\times 10^{-6}}}\\\\\Rightarrow \omega_o=\dfrac{1}{\sqrt{5}\times 10^{-3}}\\\\\Rightarrow \omega_o=0.447\times 10^{3}[/tex]
Also, frequency is given by
[tex]\Rightarrow 2\pi f=\omega_o\\\\\Rightarrow f=\frac{\omega_o}{2\pi}[/tex]
[tex]\Rightarrow f=\dfrac{1}{2\pi}\times 0.447\times 10^3\\\\\Rightarrow f=71.16\ Hz[/tex]
