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Question
How does the sign of the phase angle `phi`, by which the supply voltage leads the current in an LCR series circuit, change as the supply frequency is gradually increased from very low to very high values.
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Solution
The phase angle `phi` by which voltage leads the current in LCR series circuit where XL > XC.
`tan phi = (X_L - X_C)/R = (2pivL - 1/(2pivC))/R`
If v is small XC > XL so `[2πvL - 1/(2πvC)]` is negative, so tan `phi < 0`.
For v is large, XL > XC
So XL = XC is positive to `tan phi > 0`
For XL = XC i.e. at resonant frequency
XL – XC = 0 so `tan phi` = 0.
So phase angle in series LCR ac circuit will change from a negative to zero and then zero to positive value.
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