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NEET PHYSICSALTERNATING CURRENTMedium

Question

In a series LCR circuit, the inductance LL is 10 mH, capacitance CC is 1 μ\muF and resistance RR is 100 Ω\Omega. The frequency at which resonance occurs is:

A

1.59 kHz

B

15.9 rad/s

C

15.9 kHz

D

1.59 rad/s

Step-by-Step Solution

In a series LCR circuit, resonance occurs when the inductive reactance equals the capacitive reactance (XL=XCX_L = X_C). The resonant angular frequency is defined as ω0=1/LC\omega_0 = 1/\sqrt{LC} . The resonant frequency in Hertz is calculated using the formula ν0=12πLC\nu_0 = \frac{1}{2\pi\sqrt{LC}} . Given L=10 mH=10−2 HL = 10 \text{ mH} = 10^{-2} \text{ H} and C=1 \muF=10−6 FC = 1 \text{ \mu F} = 10^{-6} \text{ F}, we have: ν0=12π10−2×10−6=12π10−8=12π×10−4=100002π≈100006.283≈1591.5 Hz\nu_0 = \frac{1}{2\pi\sqrt{10^{-2} \times 10^{-6}}} = \frac{1}{2\pi\sqrt{10^{-8}}} = \frac{1}{2\pi \times 10^{-4}} = \frac{10000}{2\pi} \approx \frac{10000}{6.283} \approx 1591.5 \text{ Hz}, which is approximately 1.59 kHz.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from ALTERNATING CURRENT. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSALTERNATING CURRENTseriescircuitinductancecapacitanceresistance

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