In a black box of unknown elements (L or R or any other combination), an ac voltage `E=E_(0) sin (omegat)+phi)` is applied and current in the circuit was found to be `I=(I_0) sin [ omega t + phi + (pi//4)]`. Then the unknown elements in the box may be

Options

A. only capacitor
B. inductor and resistor both
C. either capacitor, resistor and inductor or only capacitor and resistor
D. only resistor

Answer

C

Explanation

If we have all `R, L` and `C` then `I` vs `E` will be

To obtain a leading phase difference of `pi//4`:
If `X_(L) lt X_(C )` and we use all `R, L` and `C` in the circuit then the resultant graph will be:
`I(X_(c ) - X_(i))`

which can give a leading phase difference of `pi//4` : Similarly, if we have only resistance and capacitor then we can obtain a phase
diferece of `pi//4` (leading) for suitable values `I, X_(C )` and `R`.
But we cannot obtain a leading phase difference `pi//4` if we use only capacitor
(phase difference of `pi//2)`, or only (inductor and resistor) phase difference of `pi//2)` or only resistor (phase difference of 0).