InterviewSolution
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InterviewSolution
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A solenoid with inductance `L=7 m H` and active resistance `R=44 Omega` is first connected to a source of direct voltage `V_(0)` and then to a source of sinusoidal voltage with effective value `V=V_(0)` . At what frequency of the oscillator will be power consumed by the solenoid be `eta=5.0 ` times less than in the former case ? |
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Answer» Correct Answer - 2 In case of direct current, `P_(DC)=V_(M)^(2)/R` The impedance of `LR` circuit is `Z=sqrt(R^(2)+X_(L)^(2))=sqrt(R^(2)+omega^(2)L^(2))` `:. I_(M)=V_(M)/Z=V_(M)/sqrt(R^(2)+omega^(2)L^(2))` `:. P_(AC)=I_(M)^(2)R=(V_(M)^(2)R)/(R^(2)+omega^(2)L^(2))` According to the problem, `P_(DC)=eta P_(AC)` or `V_(M)^(2)/R=eta (V_(M)^(2)R)/(R^(2){1+((omegaL)/R)^(2)})` or `1/R=eta/(R{1+((omegaL)/R)^(2)})` or `omega=R/L sqrt(eta^(2)-1) rArr 2piv=R/L sqrt(eta^(2)-1)` `v=R/(2pi L)sqrt(eta^(2)-1)=2kHz` |
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