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A series LCR circuit is connected to an ...

A series LCR circuit is connected to an a.c. source of variable frequency. Drow a suitable phasor diagram deduce the expressions for the amplitude of the current and phase angle.

Text Solution

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From the phasor diagram
`vec(V) = sqrt((V_(RM))^(2) + (V_(CM) - V_(LM))^(2))`
`V_(m) = sqrt([R^(2) + (X_(C) - X_(L))^(2)])`
`I_(m) = (V_(m))/(sqrt([R^(2) + (X_(C) - X_(L))^(2)])`
From the figure
`tan phi = (V_(Cm) - V_(Lm))/(V_(Rm))`
`= (I_(m)(X_(C) - X_(L)))/(I_(m)R)`
`:. phi = tan^(-) ((X_(C) - X_(L))/(R ))`
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