Question

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.

Answer 1

   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.