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Relation of voltage to current

So far we have pictured simply the voltage on the linę, but that voltage is of course accompanied by a current. We now ask what relation this current has to the voltage. To find the relation between voltage and current, we substitute v back in equation 2.6

and integrate with respect to time, and obtainwhere f(z) is the constant of integration.

We substitute this result back into equation 2.6 and obtain the result fo(z) = 0, i.e. f(z) = constant. This constant term corresponds to a steady d.c. voltage, which we set to zero, as we are not interested in a superimposed d.c. solution. Hence, the above relation becomes. A little investigation will show that the parameter Zohas the dimensions of resistance and its units are thus ohms.

It is however common to cali Zothe characteristic impedance rather than the characteristic

resistance. This is done because because we will encounter, in a later section dealing with the analysis of sinusoidal waves on a transmission linę, a concept which is

properly called characteristic impedance and which has a defining equation which is formally

identical with equation 2.12. It is traditional to recognise that homology by the use of the same terminology, even though doing so disguises the reality that in the present

context Zois really a resistance, and that in the present context the concept of

impedance

has no meaning.