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
1.59 kHz
15.9 rad/s
15.9 kHz
1.59 rad/s
The Correct Option is A
Solution and Explanation
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
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Concepts Used:
Inductance
Inductance is a key parameter in electrical and electronic circuit designs. Like resistance and capacitance, it is a basic electrical measurement that affects all circuits to some degree.
Inductance is used in many areas of electrical and electronic systems and circuits. The electronic components can be in a variety of forms and may be called by a variety of names: coils, inductors, chokes, transformers, . . . Each of these may also have a variety of different variants: with and without cores and the core materials may be of different types.
There are two ways in which inductance is used:
- Self-inductance: Self-inductance is the property of a circuit, often a coil, whereby a change in current causes a change in voltage in that circuit due to the magnetic effect of caused by the current flow. It can be seen that self-inductance applies to a single circuit - in other words it is an inductance, typically within a single coil. This effect is used in single coils or chokes.
- Mutual-inductance: Mutual inductance is an inductive effect where a change in current in one circuit causes a change in voltage across a second circuit as a result of a magnetic field that links both circuits. This effect is used in transformers.