Question

In a series LCR circuit, the inductance L is 10 mH, Capacitance C is 1μF and resistance R is 100Ω. 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

Answer 1

Answer: (A)

1.59 kHz

Answer 2

The correct option is (A): 1.59 kHz
The resonant frequency (fr) of a series LCR circuit is given by the formula:
fr = $\frac{1}{2\pi(LC)}$
where L is the inductance in Henries, C is the capacitance in farads, and π is the mathematical constant pi (approximately equal to 3.14).
Substituting the given values, we get:
$f_r=\frac{1}{2\pi\sqrt{10\,mH\times1\mu F}}$
$= \frac{1}{(2π\sqrt{(10 x 10-3 H x 10-6 F)) }}$
$= \frac{1}{(2π\sqrt{(10-8))}}$
$=\frac{1}{(2π \times 10^{-4})}$
$= \frac{1}{(6.28 \times 10^{-5})}$
= 1591.5 Hz (approx)
Therefore, the resonant frequency of the series LCR circuit is approximately 1591.5 Hz, = 1.59K Hz