Question

In series LCR circuit, the resonance occurs at one frequency only. At resonance the inductive reactance is equal and opposite to the capacitive reactance.

• A. It both Assertion and Reason are true and the Reason is a correct explanation of the Assertion
• B. If both Assertion and Reason are true but Reason is not a correct explanation of the Assertion
• C. If Assertion is true but the Reason is false
• D. If both Assertion and Reason are false

Answer 1

Answer: (A)

It both Assertion and Reason are true and the Reason is a correct explanation of the Assertion

Answer 2

For resonance to occur, the net reactance of the circuit should be zero. Hence in that condition $X_{ C }-X_{ L }=0$ $\therefore \frac{1}{\omega C}-\omega L=0$ $\Rightarrow \omega L=\frac{1}{\omega C}$ $\Rightarrow \omega^{2}=\frac{1}{L C}$ $\Rightarrow \omega=\frac{1}{\sqrt{L C}}$ $\Rightarrow f=\frac{1}{2 \pi \sqrt{L C}}$ Hence resonance occurs at a single frequency and at resonance the inductive reactance is equal and opposite to the capacitive reactance.