Which one of the following curves represents the variation of impedance $(Z)$ with frequency $f$ in a series $L-C-R$ circuit, when connected to an AC source?

• A

  
  
• B

  
  
• Correct answer
  C

  
  
• D

  
  

Solution

Impedance $(Z)$ of a series $L-C-R$ circuit is given as
$=\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)^2}$
At $X_L=X_C$, then from Eq. (i), $Z_{\min }=R$, and $f=f_0 \quad\left[f_0=\right.$ resonance frequency $]$ Hence, the variation of $Z$ with frequency $f$ in a series $L-C-R$ circuit is given as

Hence, the correct answer is option: 'C'.