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Alternating Current — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current1 Mark
MCQ
For two statements are given-one labelled Assertion $(A)$ and the other labelled Reason $(R).$ Select the correct answer to these questions from the codes $(a), (b), (c)$ and $(d)$ as given below.
Assertion: At resonance, $\text{LCR}$ series circuit have a maximum current.
Reason: At resonance, in $\text{LCR}$ series circuit, the current and e.m.f are in phase with each other.
  • A
    Both $A$ and $R$ are true and $R$ is the correct explanation of $A.$
  • ✓
    Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
  • C
    $A$ is true but $R$ is false.
  • D
    $A$ is false and $R$ is also false.
✓

Answer

Correct option: B.
Both $A$ and $R$ are true but $R$ is not the correct explanation of $A$.
At resonance $X_L = X_C$ or $\omega\text{L}=\frac{1}{\omega\text{C}}.$
Because of this impedance of $\text{LCR}$ series circuit become equal to resistance of circuit $\Big(\text{Z}=\sqrt{\text{R}^2+(\text{X}_\text{L}-\text{X}_\text{C})^2}\Big).$
Therefore from $\text{I}=\frac{\text{E}}{\text{Z}}=\frac{\text{E}}{\text{R}},$ at resonance, current in $\text{LCR}$ series circuit is maximum.
Correspondingly phase angle is also equal to zero.
Therefore emf and current are in phase in $\text{LCR}$ series circuit.

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