# When an AC source of emf e=E sin(100t) is connected across a circuit, phase difference between the emf e and current I in the circuit is observed to be π/4.If the circuit consists of possibly R_L or R_C or L_C in series find the relationship between two elements.

1
by TimsyPrabhakar888

2015-09-16T04:08:17+05:30

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e = E Sin 100 t    =>  ω = 100 rad/sec

1)  R L circuit:

Z = √ [R² + XL² ]
I = (E /Z)  Sin (ω t + Ф)        where    tan Ф = - XL / R      So Ф is negative.
So  XL = R  as     Ф = π/4
R = ω L = 100 L

2) RC  circuit
i = (E / Z)  Sin (ω t + Ф)       where  Z  = √ [R² + Xc²]
tan Ф = Xc / R = 1/(RωC)  = tan π/4 = 1
So  R = 1/(ωC)

3)
LC  case:
Here  the phase difference between the current and the voltage is 90 deg.  It is leading or trailing depends on the values o f  XL  and Xc.  Which ever is more or less.