$4\mathrm{.}2$ Linearity Property

${?}_{}$ Linearity is the property of an element describing a linear relationship between cause $($input and$/$or excitation$)$ and effect $($output and$/$or response$).$

$AB$ By the linearity property both the homogeneity $($scaling$)$ property and the additiv property ought to hold good.

$in$ For a resistor, for instance, Ohm's law relates the input $i$ to the output $v,$ giver by the equation of the form,

By the homogeneity property, if the current is increased by a constant $k,$ then th voltage increases correspondingly by $k$; that is$,$

$R(ki)=kv$

$in$ By the additivity property, the response to a sum of inputs is the sum of the responses to each input applied separately, that is$,$ if

and

$v_2=R{i}_2$

Department of Electrical & Electronic Engineering, School of Engineering, University of Zambia