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, V_R , V_L and V_C are the voltages across R, L and C respectively where I_R , I_L  and I_C  are 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