A series LCR circuit connected to an AC source with voltage of the source $v=v_m \sin \omega t$.
If 'q' is the charge on the capacitor and 'i' is the current, from Kirchoff's loop rule:
$L \frac{d i}{d t}+i R+\frac{q}{c}=V$
The current in the circuit is given by $i=I_{m} \sin (\omega t+\phi)$ where $\phi$ is the phase difference between the voltage across the source and current in the circuit.
We know $V_{R m}=L_m R ; V_{L m}=L_m X_L ; V_{C m}=L_m X_C$; and $X_L=\omega L ; X_C=\frac{1}{\omega C}$
Total impedance in the circuit regulates current. At resonance frequency of the LCR circuit current in the circuit is maximum.
Given below are two statements
Statement I: In an LCR series circuit, power dissipated is minimum at resonance.
Statement II: In an LCR circuit, power is dissipated only in the inductor and capacitor.
In the light of the above statements, choose the most appropriate answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both Statement I and Statement II are false
In LCR series circuit, $P_{avg} =V_{\text {rms }} \times I_{\text {rms }} \times \cos \phi$ at resonance, $\phi=0^{\circ}, \Rightarrow \cos \phi=1 \Rightarrow$ hence power dissipated is maximum at resonance.
In LCR circuit, power is dissipated only across the resistor.
Hence both the statements are false.