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  4. In a black box of unknown elements ( L or R or any other combination), an ac voltage E=E0 sin (ω t+φ) is applied and current in the circuit was found to be I=I0 sin [ω t+φ+(π / 4)]. Then the unknown elements in the box may be </br><img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/9224998d880c9449a00ef94f4f2890c8-.png />

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Q. In a black box of unknown elements ( $L$ or $R$ or any other combination), an ac voltage $E=E_{0} \sin (\omega t+\phi)$ 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
image

Alternating Current

Solution:

Since current is leading emf, capacitor must be present in the circuit. Along with capacitor, there can be either (i) only resistor or (ii) resistor and inductor if $X_{ C }>X_{ L }$.
In both of the above conditions, we can obtain a phase difference of $\pi / 4$ with current leading emf.