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 |

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