Linearity Property & Source Transformation

| Linearity Property |

A linear element or circuit satisfies the properties of

| Additivity |

 requires that the response to a sum of  inputs is the sum of the responses to each input  applied separately.

If v1 = i1R and v2 = i2R

then applying (i1 + i2)

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

| Homogeneity |

If you multiply the input (i.e. current) by some  constant K, then the output response (voltage) is
scaled by the same constant.

If v1 = i1R

then K v1 =K i1R

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

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| Source Transformation |

What is Source Transformation ?

A source transformation is the process of replacing a voltage source vs in series with a resistor R by a current source is in parallel with a resistor R, or vice versa

Equivalent sources can be used to simplify the analysis of some circuits.

A voltage source in series with a resistor is transformed into a current source in parallel with a resistor.

 A current source in parallel with a resistor is transformed into a voltage source in series with a resistor. 

EXAMPLE 

| My Learning Experience XD |

I learned that in Linearity Property a circuit is linear if the output is linearly related with its input. Thus, The relation between power and voltage is nonlinear. So this theorem cannot be applied in power. We can say that a resistor is a linear element. Because the voltage-current relationship satisfies both the additivity and the homogeneity properties. In Source Transformation I noted that keep the polarity of the voltage source and the 

direction of the current source in agreement and Source transformation also applies to dependent sources.