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How does the sign of the phase angle phi...

How does the sign of the phase angle `phi`, by which the supply voltage leads the current in an LCR serices circuit, change as the supply frequency is gradually increased from very low to very high values ?

Text Solution

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Let `phi` be the phase angle by which voltage leads the current in an LCR circuit .
Let `X_(L)` be the reactance offered by inductance, L, `X_(C)` be the reactance offered by capacitance C, R be the resistance in the circuit and `omega` be the angular frequency , them
tan `phi = (X_(L) - X_(C))/(R) = ( omega L - (1)/(omega C) )/(R)`
If omega is lower than resonant frequency `(omega_(0))` tan `phi` is negative which means `phi` is negative when `omega = omega_(0)`,
`omega L = (1)/(omega C)` , which gives tan `phi` = 0
`therefore " " phi` = 0
when `omega` is higher than resonant frequency , tan `phi` is positive which means `phi` is positive.
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