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The resistance of an R-L A.C. circuit is 10 Omega. An emf E_0 applied across the circuit at omega=20 rad/s . If the current in the circuit is I_0/sqrt2 what is the value of L ? |
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Answer» 0.55 H `omega`=20 rad/s `I=I_0/sqrt2` `rArr` Impedence of series connection of R-L `|Z|=sqrt(R^2+(omegaL)^2)` Current in CIRCUIT `I=E_0/"|Z|"` `I_0/sqrt2=E_0/(R(sqrt(1+((omegaL)/R)^2)))` `I_0/sqrt2=I_0/sqrt(1+((omegaL)/R)^2)[because E_0/R=I_0]` `therefore 1/sqrt2=1/sqrt(1+((omegaL)/R)^2)` `therefore 2=1+((omegaL)/R)^2` `therefore 1=((omegaL)/R)^2` `therefore 1=(omegaL)/R` `therefore L=R/omega` `therefore L=10/20` `therefore` L=0.5 H |
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