Question

Resonance occurs in a series $LCR$ circuit when the frequency of the applied emf is $1000Hz$.

• A. when frequency $=900Hz$, then the current through the voltage source will be ahead of emf of the source
• B. the impedance of the circuit is minimum at $f=1000Hz$
• C. at only resonance the voltages across $L$ and $C$ differ in phase by $180^{\circ }$
• D. if the value of $C$ is doubled, resonance occurs at $f=2000Hz$

Answer 1

Answer: (A), (B)

$(f=900Hz)<\left(f_{\text{res }}=1000Hz\right)$,
so $X_c>X_L$, circuit becomes capacitive and current leads emf.
At resistance, impedance is minimum.
Not only at resonance, but at all conditions voltage across $L$ and $C$ differs in phase by $180^{\circ }$ when connected in series.