Question

obtain the v-I relationship for passive element

Answer 1

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 VCare the voltages across R, L and C respectively where IR , IL  and IC  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 



Answer 2

Passive elements are the important components of the electric circuit like Resistors, capacitors, Transformers, Inductors etc.
Passive elements cannot generate or amplify an electrical signal.

V-I Relation ship :
************************************************************************************
Resistance : R
Resistance is the passive element that opposes the flow of electrons through it.Resistance Si units : Ohms

By Ohm's Law :
R=V/I
where V is the Voltage across the resistor and I is the current flowing the resistor.

Inductance is denoted by L .
It is the passive element used for the storage of the energy in the form of electro magnetic field.
V(t)=Ldi(t)/dt

Capacitance :Denoted by C
A capacitor store the energy electrostatically as a charge across its plate.
I(t)=Cdv(t)/dt***************************************************************************************