Question

A $12\Omega$ resistor, a $40\mu F$ capacitor, and an $8mH$ coil are in series across an ac source. The resonant frequency is

• A. $28.1Hz$
• B. $281Hz$
  
• C. $2,810Hz$
  
• D. $10Hz$
  

Answer 1

The correct option is B $281Hz$

$\omega =\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{8\times {10}^{-3}\times 40\times {10}^{-6}}}$

$⟹\omega =\frac{{10}^4}{\sqrt{32}}$

$\omega =2\pi \nu$ where $\nu$=frequency

frequency$=\nu =\frac{\omega }{2\pi }=\frac{{10}^4}{2\times 3.143\times \sqrt{32}}$

$⟹\nu =281Hz$

Answer-(B)