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Statement 1: In the purely resistive ele...

Statement 1: In the purely resistive element of a series LCR, ac circuit the maximum value of rms current increase with increase in the angular frequency of the applied emf.
Statement 2: `I_(max)=(epsilon_(max))/(Z), Z=sqrt(R^(2)+(omega L-(1)/(omega C)^(2)))`,
where `(I_(max))` is the peak current in a cycle.

A

Statement 1 is true, statement 2 is true, Statement 2 is the correct explanation for statement 1.

B

Statement 1 is True, Statement 2 is true , Statement 2 is NOT the correct explanation for Statement 1

C

Statement 1 is True, Statement 2 is False.

D

Statement 1 is False, Statement 2 is true

Text Solution

Verified by Experts

The correct Answer is:
D
The maximum value of rms current `=(epsilon_(rms))/(Z) =(epsilon_(rms))/(R )`. It does not depend upon `omega`.
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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) (b) How does impedance of the circuit changes with omega

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) (a) (a) Draw graphs showing variation of current amplitude of a LCR series circuit with frequency w of driving omega lt omega_(0) , alternating voltage.

Knowledge Check

  • The resonant frequency of a series LCR circuit with L=2.0 H,C =32 muF and R=10 Omega is

    A
    20 Hz
    B
    30 Hz
    C
    40 Hz
    D
    50 Hz

  • In R-L-C series circuit, we have same current at angular frequencies omega_(1) and omega_(2) . The resonant frequency of circuit is

    A
    `(omega_(1)^(2))/(omega_(2))`
    B
    `(omega_(2)^(2))/(omega_(1))`
    C
    `sqrt(omega_(1) omega_(2))`
    D
    `omega_(1) + omega_(2)`

  • The current in a circuit containing a capacitance C and a resistance R in series leads over the applied voltage of frequency omega/(2pi) by.

    A
    `tan^(-1)(1)/(omegaCR)`
    B
    `tan^(-1)(omegaCR)`
    C
    `tan^(-1)(omega1)/R`
    D
    `cos^(-1) (omegaCR)`

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