Voltage Current Relationships For Passive Elements

       The voltage current relationships for the passive elements resistance (R), inductance (L) and capacitor (C) are given in the table below,

       Note that in the table above, VR , VL and VC are the voltages across R, L and C respectively where IR , I and Iare the currents through R, L and C respectively.

Example  : 
       A current waveform flowing through an inductor of 1mH is shown in the fig. 1. Obtain and sketch the waveform of the voltage across the inductor.
Fig.  1

Solution : From the given waveform,
       For 0 < t < 2, i(t) is a straight line of slope = 100/2 = 50

       ...                    i(t)  = 50 and  di(t)/dt = 50                             ... 0 < t < 2

       For 2 < t < 4, i(t) = 100 and di(t)/dt = 0 

       For 4 < t < 6, i(t) is a straight line of slope = - 100/2 = 50 

        ...                   i(t) = -50t and di(t)/dt = -50                                 ... 4 < t < 6

                                     = 1 x 10-3 x 50 = 0.05 V                                    ... 0 < t < 2

                                     = 1 X 10-3 X 0 = 0                                            ... 2 < t < 4

                                     = 1 x 10-3 x (-50) = -0.05 V                              ... 4 < t < 6

       The waveform shown in the fig . 2 
Fig.   2

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