• question_answer Direction: A voltage source $V={{V}_{0}}\,\sin \,(100t)$ is connected to a black box in which there can he either one element out of L, C, R or any two of them connected in series. At steady state the variation of current in the circuit and the source voltage are plotted together with time, using an oscilloscope, as shown. The element(s) present in black box is/are A)  only C                         B)  L and C           C)  L and R                      D)  L and C

$\Delta \theta =\omega \Delta t=\frac{\pi }{4}$ $\tan \,\theta =\frac{X}{R}$ $\Rightarrow$            $X=R$ Since, current leads the voltage the circuit consists of R and C. and      ${{i}_{0}}=\frac{{{V}_{0}}}{z}$ $\therefore$    $z=\frac{{{V}_{0}}}{{{i}_{0}}}=\frac{100}{\sqrt{2}}=50\sqrt{2}$ Now,    $R\sqrt{2}=50\sqrt{2}$ $\Rightarrow$            $R={{X}_{C}}=50$ ${{X}_{C}}=\frac{1}{C\omega }=50$ $\Rightarrow$            $C=\frac{1}{50\,\omega }=200\,\mu F$ $\tau =RC=50\times 200\times {{10}^{-6}}=1\times {{10}^{-2}}s$
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