$4\mathrm{.}2$ Linearity Property Cont'd

G Then applying $(i_1+i_2)$ yields,

$v=R(i_1+i_2)=R{i}_1+R{i}_2=v_1+v_2$

a Thus, a resistor is said to be a linear element because the voltage$-$current relationship satisfies both the homogeneity and the additivity properties.

of In general, a circuit is linear if and only if it is both additive and homogeneous.

A$.$ A linear circuit is one whose output is linearly related $($or directly proportional$)$ to its input.

Ar In this course the scope shall be limited to only linear circuits.

Oote that since $p=R{i}^2=\frac{v^2}{R}($making it a quadratic function rather than a linear one$),$ the relationship between power and voltage $($or current$)$ is nonlinear.

Therefore, the theorems which shall be covered in this course are not applicable to power.

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