Question

Assertion $\left(A\right)$: In series $\text{LCR}$ resonance circuit, the impedance is equal to the ohmic resistance.

Reason $\left(R\right)$: At resonance, the inductive reactance is equal and opposite to the capacitive reactance.

• A. Both $\left(A\right)$ and $\left(R\right)$ are true, and $\left(R\right)$ is the correct explanation of $\left(A\right)$
• B. Both $\left(A\right)$ and $\left(R\right)$ are true, and $\left(R\right)$ is not the correct explanation of $\left(A\right)$
• C. $\left(A\right)$ is true but $\left(R\right)$ is false
• D. $\left(A\right)$ is false but $\left(R\right)$ is true

Answer 1

The correct option is A Both $\left(A\right)$ and $\left(R\right)$ are true, and $\left(R\right)$ is the correct explanation of $\left(A\right)$

For resonance Condition in $\text{LCR}$ circuit,

$X_L=X_C$

The net impedance of the circuit is,

$Z=\sqrt{R^2+(X_L-X_C{)}^2}$


$\Rightarrow Z=R$


As we can see, $X_L\text{and}{X}_C$ are in opposite direction. Hence, phase difference between them is $\varphi ={180}^{\circ }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.