Question

Resonance occurs in a series L-C-R circuit when the frequency of the applied emf is $1000\text{Hz}$. Then :

• A. when $f=900\text{Hz}$, the circuit behaves as a capacitative circuit
• B. the impedance of the circuit is maximum at $f=1000\text{Hz}$
• C. at resonance the voltage accross $L$ and voltage accross $C$ differ in phase by ${180}^{\circ }$
• D. if the value of $C$ is doubled resonance occurs at $f=2000\text{Hz}$

Answer 1

Answer: (A), (C)

The correct options are
A when $f=900\text{Hz}$, the circuit behaves as a capacitative circuit
C at resonance the voltage accross $L$ and voltage accross $C$ differ in phase by ${180}^{\circ }$

At resonance $X_L=X_C$ and $Z=Z_{\text{min}}=R$
$X_L=\omega L$ and $\frac{1}{\omega C}=X_C$
If $‘f^{\prime }$ is decreased then ${}^{\prime }{\omega }^{\prime }$ will decrease and hence $X_C$ will increase therefore at $f<f_r$, circuit behaves as capacitive.
$V_L$ and $V_C$ always differ in phase by ${180}^{\circ }$ at any frequency.
$f=\frac{1}{2\pi \sqrt{LC}}$
Increasing $C$ decreases $f$