The growth in areas of application of electric circuits has led to an evolution of simple to complex circuits. Engineers over the years have developed some theorems to simplify circuit analysis to handle the complexity of circuits.
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 requires that if the input (also called the excitation) is multiplied by a constant, then the output (also called the response) is multiplied by the same constant.
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.
We can tell a circuit is linear if the circuit both the additive and the homogeneous. A linear circuit always consists of linear elements, linear independent and dependent sources.
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.