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A sinusoidal voltage of frequency 60Hz a...

A sinusoidal voltage of frequency `60Hz` and peak value `150V` is applied to a series `L-R` circuit, where `R=20Omega` and `L=40mH`
(a) compute `T, omega, X_L, Z` and `phi`
(b) Compute the amplitudes of current `V_R` and `V_L`

Text Solution

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(a) `T=1/f=1/60s`
`omega=2pif=(2pi)(60)=377rad//s`
`X_L=omegaL=(377)(0.040)`
`=15.08Omega`
`Z=sqrt(X_L^2+R^2)`
`=sqrt((15.08)^2+(20)^2)`
`=25.05Omega`
`phi=tan^-1(X_L/R)=tan^-1(15.08/20)=tan^-1(0.754)`
`=37^@`
(b) Amplitudes (maximum value) are
`i_0=V_0/Z=150/25.05~~6A`
`(V_0)_R=I_0r=(6)(20)=120V`
`(V_0)_L=i_0X_L`
`=(6)(15.08)=90.5V`
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