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A series combination of an inductor of s...

A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of `V=V_0sinomegat`. The current through the circuit is `I=I_0sin(omegat-theta)`,where `I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2))`and`theta=tan^-1 ""1/R(omegaL-1/(omegaC))`.
Now that, the frequency of both voltage and current is `f=omega/(2pi)` . The rms value of these parameters during one complete cycles are `V_(rms)=V_0/sqrt2`and`I_(rms)=I_0/sqrt2` respectively. These values are shown in alternating voltmeter and ammeter.
The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is `overlineP=V_(rms)I_(rms)costheta`. This `costheta` is termed the power factor.
`V=V_0sinomegat` electromotive force is applied to an alternating circuit consisting of resistance R' and an inductor of self-inductance L. The phase difference between the voltage and current is

A

`90^@`

B

`tan^-1""(omegaL)/(R')`

C

`tan^-1""(R')/(sqrt(R'^2+omega^2L^2))`

D

`sqrt(R'^2+omega^2L^2)/(R')`

Text Solution

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The correct Answer is:
B
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Find the r.m.s. value of alternating current over a complete cycle.

A device X is connected across an ac source of voltage V=V_0sinomegat . The current through X is given as I=I_0sin(omegat+pi/2) . Device X is a capacitor.

Knowledge Check

  • A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of V=V_0sinomegat . The current through the circuit is I=I_0sin(omegat-theta) ,where I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2)) and theta=tan^-1 ""1/R(omegaL-1/(omegaC)) . Now that, the frequency of both voltage and current is f=omega/(2pi) . The rms value of these parameters during one complete cycles are V_(rms)=V_0/sqrt2 and I_(rms)=I_0/sqrt2 respectively. These values are shown in alternating voltmeter and ammeter. The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is overlineP=V_(rms)I_(rms)costheta . This costheta is termed the power factor. the power factor of the circuit is question (i) is

    A
    zero
    B
    `(omegaL)/(R')`
    C
    `(R')/(sqrt(R'^2+omega^2L^2))`
    D
    `(sqrt(R'^2+omega^2L^2))/(R')`

  • A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of V=V_0sinomegat . The current through the circuit is I=I_0sin(omegat-theta) ,where I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2)) and theta=tan^-1 ""1/R(omegaL-1/(omegaC)) . Now that, the frequency of both voltage and current is f=omega/(2pi) . The rms value of these parameters during one complete cycles are V_(rms)=V_0/sqrt2 and I_(rms)=I_0/sqrt2 respectively. These values are shown in alternating voltmeter and ammeter. The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is overlineP=V_(rms)I_(rms)costheta . This costheta is termed the power factor. The power factor of the circuit in question (iii) is

    A
    -1
    B
    zero
    C
    between zero and 1
    D
    1

  • A series combination of an inductor of self-inductance L, capacitor of capacitance C and resistor R is connected to an alternating voltage source of V=V_0sinomegat . The current through the circuit is I=I_0sin(omegat-theta) ,where I_0=V_0/(sqrt(R^2+(omega-1/(omegaC))^2)) and theta=tan^-1 ""1/R(omegaL-1/(omegaC)) . Now that, the frequency of both voltage and current is f=omega/(2pi) . The rms value of these parameters during one complete cycles are V_(rms)=V_0/sqrt2 and I_(rms)=I_0/sqrt2 respectively. These values are shown in alternating voltmeter and ammeter. The power consumed by the circuit P=VI. The mean value i.e., the effective power of the circuit in a complete cycle is overlineP=V_(rms)I_(rms)costheta . This costheta is termed the power factor. Which element is responsible for the power consumption in an alternating current circuit?

    A
    only resistor
    B
    only inductor
    C
    only capacitor
    D
    resistor,inductor and capacior

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    A device X is connected across an ac source of voltage V=V_0sinomegat . The current through X is given as I=I_0sin(omegat+pi/2) . Draw the phasor diagram for the device X.

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