Linearity Property

Linear Property is the linear relationship between cause and effect of an element. This property gives linear and nonlinear circuit definition. The property can be applied in various circuit elements. The homogeneity (scaling) property and the additivity property are both the combination of linearity property.

The homogeneity property is that if the input is multiplied by a constant k then the output is also multiplied by the constant k. Input is called excitation and output is called response here. As an example if we consider ohm’s law. Here the law relates the input i to the output v.

      Mathematically,                                          v= iR

If we multiply the input current  i by a constant k then the output voltage also increases correspondingly by the constant k. The equation stands,     

 kiR = kv

The additivity property is that the response to a sum of inputs is the sum of the responses to each input applied separately.

Using voltage-current relationship of a resistor if

                           v₁ = i₁R       and   v₂ = i₂R

Applying (i₁ + i₂)gives

                             V = (i₁ + i₂)R = i₁R+ i₂R = v₁ + v₂

We can say that a resistor is a linear element. Because the voltage-current relationship satisfies both the additivity and the homogeneity properties.

A circuit is linear if the output is linearly related with its input.

The relation between power and voltage is nonlinear. So this theorem cannot be applied in power.