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In an LCR circuit , L = 88 mH and C = 1m...

In an LCR circuit , L = 88 mH and C` = 1muF` and the value of the resistor is unknown . The AC source has a frequency of 1000 Hz and the phase between emf and current is `70^@` . Calculate the value of R of the resistor .

Text Solution

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`tan phi = (X_L - X_C)/(R )`
` R = (X_L - X_C)/( tan phi) `
`phi = 70^@ , omega = 2pi f = 2pi xx 1000 = 2000 pi , L = 88 xx 10^(-3) H , C = 1 xx 10^(-6) F`
` X_L = omega L = 2000 xx 3.14 xx 88 xx 10^(-3) = 553 Omega`
` X_C = (1)/(omega C) = (1)/(2000 xx 3.14 xx 10^(-6) ) = (10^6)/(2000 xx 3.14) = (1000)/(2 xx 3.14)`
`X_C = 159 Omega`
` R = (X_L - X_C)/(tan phi) = (533 - 159)/(tan 70) = (394)/(2.75) = 143 Omega `
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