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A device X is connected across an ac sou...

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)`.
Identify the device X and write the expression for its reactance.

Text Solution

Verified by Experts

Device X is a capacitor
`therefore` Capacitive reactance , `X_C=1/(omegaC)=1/(2pifC)`
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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) . Device X is a capacitor.

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.

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))`
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  • 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

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    -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. The voltage applied in an LCR circuit having R=10Omega,L=10mH and C=1muF is V=20sinomegat volt. For what frequency of the applied voltage will the current reach its peak value?

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    159 Hz
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    1592 Hz
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    `1.59times10^4Hz`
    D
    `1.59times10^5Hz`

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