A resistor R and an inductor L are connected in series to a 24 V, 50 Hz supply. A current of 1 A flows through the circuit. If the current differs in phase from the applied voltage by \( 60^\circ \), the value of impedance in the circuit is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 24\,\Omega \)
The impedance of an ac circuit is the ratio of the voltage to the current.
\( \displaystyle Z = \frac{V}{I} = \frac{24\,\mathrm{V}}{1\,\mathrm{A}} = 24\,\Omega \)
The phase angle is not needed for \( Z \). It can be used to check the parts: \( R = Z\cos 60^\circ = 12\,\Omega \) and \( X_L = Z\sin 60^\circ \approx 20.8\,\Omega \). Neither of these is the impedance.
Note: NTA dropped this question and gave full marks to every candidate, because none of the printed options was \( 24\,\Omega \): they were \( 21\,\Omega \), \( 12\,\Omega \), \( 17\,\Omega \) and \( 6\,\Omega \). Option (1), printed as \( 21\,\Omega \), has been changed to \( 24\,\Omega \) so that the question has one correct answer, for the benefit of students.