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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: When capacitive reactance is smaller than the inductive reactance in $\text{LCR}$ series circuit, e.m.f. leads the current.
Reason: The phase angle is the angle between the alternating e.m.f. and alternating current of the circuit.
  • 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 $A.$
The phase angle for the $\text{LCR}$ series circuit is given by $\tan\theta=\frac{\text{X}_\text{L}-\text{X}_\text{C}}{\text{R}}=\frac{\frac{\omega\text{L-1}}{\omega\text{C}}}{\text{R}}.$
Where $X_L, X_C$ are inductive reactance and capacitive reactance respectively.
When $X_L > X_C$ then $\tan\theta$ is positive
i.e. $\theta$ is positive $\big($between $0$ and $\frac{\pi}{2}\big).$ Hence emf leads the current.

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