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In a series LCR circuit, the inductance ...

In a series LCR circuit, the inductance L is 10 mH, capacitance C is `1 muF` and resistance R is `100 Omega`. The frequency at which resonance occurs is:

A

15.9 kHz

B

1.59 rad/s

C

1.59 kHz

D

15.9 rad/s

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In a seris LCR circuit, the inductive reactance (X_(L)) is 10 Omega and the capacitive reactance (X_(C)) is 4 Omega . The resistance (R) in the circuit is 6 Omega. The power factor of the circuit is :

Read the following passage and then answer questions on the basis of your under standing of the passage and the related studied concepts. Passage: For an LCR series circuit driven with an alternating voltage of amplitude Vmand angular frequency oo, the current amplitude is given as I_(m) =V_(m)/z = V_(m)/sqrt(R^(2) + (X_(L)-X_(C))^(2)) =V_(m)/sqrt(R^(2) + (Iomega -1/(c omega))^(2)) If omega is varied then for a particular frequency omega_(0), X_( C) = X_(L) and then Z = R and hence, I_(m) = V_(m)/R is maximum. This frequency is called the resonant frequency. The resonant frequency omega_(0) = 1/sqrt(LC) = Resonance of a LCR series a.c. circuit is said to be sharping current amplitude Im falls rapidly on increasing/decreasing the angular frequency from its resonant value 0. Mathematically, sharpness of resonance is measured by the quality factor of the circuit, which is given as: Q = (omega L)/R = 1/R sqrt(L/C) (e) An alternating series LCR circuit consists of an inductance of 10 mH, a capacitance of 100 uF and a resistance of 5 Omega . Compute its resonance frequency w, as well as the Q-factor.

Knowledge Check

  • A series LCR circuit contains inductance 5mH , capacitance 2muF and resistance 10Omega . If the frequency of A.C. source is varied, what is the frequency at which maximum power is dissipated?

    A
    `(10^(5))/(pi)Hz`
    B
    `(10^(-5))/(pi)Hz`
    C
    `(2)/(pi)xx10^(5)Hz`
    D
    `(5)/(pi)xx10^(3)Hz`

  • A series L-C-R circuit contains inductancle 5 mH, capacitor 2muF and resistance 10 Omega . If a frequency AC source is varied, then what is the frequency at which maximum power is dissipated?

    A
    `(10^(5))/(pi)` Hz
    B
    `(10^(5))/(pi)`Hz
    C
    `2/3 xx 10^(5)` Hz
    D
    `5/pi xx 10^(3)` Hz

  • If resistance R = 10 Omega , inductance L = 2 mH and capacitance C = 5 muF are connected in series to an AC source of frequency 50 Hz, then at resonance the impedance of circuit is

    A
    Zero
    B
    `10 Omega`
    C
    `1000 Omega`
    D
    `10 K Omega`

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