question_answer

If in an R-L circuit, \[{{X}_{L}}=100\Omega \] and \[R=100\,\Omega ,\] then in this circuit:

A)  current leads the potential difference in phase by \[90{}^\circ \]

B)  current lags behind the potential difference in phase by \[45{}^\circ \]

C)  current leads the potential difference in phase by \[45{}^\circ \]

D)  current and potential difference are in same phase

Correct Answer: B

Solution :

In an A.C. R-L circuit, the potential difference \[({{V}_{R}})\]across resistor is m phase with current (f) and potential difference\[({{V}_{L}})\]across inductor leads the current (i) in phase by \[90{}^\circ \]. Let V be the resultant of \[{{V}_{L}}\] and \[{{V}_{R}}\] and \[\phi \] is the angle between resultant potential difference and current. \[\therefore \]  \[\tan \,\phi =\frac{{{X}_{L}}}{R}\]                 \[\tan \,\phi =\frac{100}{100}=1\Rightarrow \phi =45{}^\circ \] Therefore, current lags behind the potential difference by \[45{}^\circ \].