MCQ
Given below are two statements :

Statement $I$ : In an $LCR$ series circuit, current is maximum at resonance.

Statement $II$ : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above statements, choose the correct from the options given below :

  • A
    Statement $I$ is true but Statement $II$ is false
  • B
    Statement $I$ is false but Statement $II$ is true
  • Both Statement $I$ and Statement $II$ are true
  • D
    Both Statement $I$ and Statement $II$ are false

Answer

Correct option: C.
Both Statement $I$ and Statement $II$ are true
c
c
Statement-$I$

$\mathrm{I}_{\mathrm{m}}=\frac{\mathrm{V}_{\mathrm{m}}}{\sqrt{\mathrm{R}^2+\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)^2}}$ at resonance $\mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{C}}$

Thus, $I_m=\frac{V_m}{R}$

$\because$ Impendence is minimum therefore $I$ is maximum at resonance.

Statement-$II$

$\mathrm{I}=\left(\frac{\mathrm{V}}{\mathrm{R}}\right)$ in purely resistive circuit.

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