Statement: The current flowing through any resistor is directly proportional to the voltage applied to it.
Mathematically, V = IR
Kirchhoff’s Current law
We all know that current is a basic feature of circuits which exists due to flow of charges. Kirchhoff’s current law explains the behavior of current at any junction.
Statement: The current flowing towards any junction (node) is equal to the current flowing away from that node.
Mathematically, ∑ Current In = ∑ Current out.
In other words, this law is also called the law of conservation of charge.
Kirchhoff’s Voltage law
Like Kirchhoff’s first law is focused on current at any junction, the voltage law explains the behavior of voltage around a loop.
Statement: The sum of voltage rise along a closed loop is equal to the sum of voltage drops around that loop.
Mathematically, ∑ Voltage rise = ∑ Voltage drop
In other words, this law is also called the law of conservation of energy.
Many electrical circuits contain a single source powering different resistors. Sometimes a circuit contain multiple current and voltage sources. A superposition principle is applied to all circuits having multiple sources.
Statement: The voltage or current appearing across any component is equal to the sum of individual voltage or current of all independent sources.
Statement: Any complex electrical circuit can be reduced to a single voltage source having a single series resistor.
Practically, the Thevenin’s and Norton’s theorems are used in analysing the properties of electrical and electronic systems. They are employed in modelling transmission lines and large complex systems.
Statement: Any complex electrical circuit can be reduced to a single current source having a single parallel resistor.
Maximum Power Transfer Theorem
Statement: if the value of load resistor is equal to the single resistor ( as calculated from Norton or Thevenin theorem) the load resistor will receive the maximum power.
Statement: Any electrical branch can be substituted with an equivalent electrical branch provided that current and voltage of both branches are same.
The Millman’s theorem is applied to the circuits which have several voltage sources in the parallel configuration. According to this theorem, the voltages source in parallel branches can be replaced by equivalent current sources and parallel resistors which can then be reduced to a single voltage source and a series resistors. The same is also true for several current sources in series configuration.