Practicing Success
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. |
Both Statement I and Statement II are true Both Statement I and Statement II are false Statement I is correct but Statement II is false Statement I is incorrect but Statement II is true |
Both Statement I and Statement II are false |
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. |