Electrical Laws

Electrical Laws

Ohm’s law

Ohm’s law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor.

Mathematically form

v ∝ i

Georg Simon Ohm defined the constant of proportionality for a resistor to be the resistance, R. (The resistance is a material property which can change if the internal or external conditions of the element are altered, e.g., if there are changes in the temperature.)

v =Ri

Kirchhoff’s Laws

Branch:A branch represents a single element such as a voltage source or a resistor.

Node:A node is the point of connection between two or more branches.

Loop:A loop is any closed path in a circuit.

Theorem of network topology:A network with b branches, n nodes, and l independent loops will satisfy the fundamental theorem of network topology:

b = l+n-1

Series:Two or more elements are in series if they exclusively share a single node and consequently carry the same current.

Parallel:Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them.

There are two Kirchhoff’s Laws

Kirchhoff’s current law (KCL)

Kirchhoff’s voltage law (KVL)

Kirchhoff’s current law (KCL)

Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering a node (or a closed boundary) is zero.

OR

The sum of the currents entering a node is equal to the sum of the currents leaving the node.

Kirchhoff’s current law is based on the law of conservation of charge, which requires that the algebraic sum of charges within a system cannot change.

Mathematically, KCL implies that

where N is the number of branches connected to the node and is the nth current entering (or leaving) the node.

Kirchhoff’s voltage law (KVL)

Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.

OR

Sum of voltages drops = Sum of voltages rise

Kirchhoff’s second law is based on the principle of conservation of energy:

Expressed mathematically, KVL states that

where M is the number of voltages in the loop (or the number of branches in the loop) and is the mth voltage.