BASIC LAWS Ohm’s Law Kirchhoff’s Law Series resistors & voltage division Parallel resistors & current division Y - transformation

Ohm’s Law Property of a material to resist a flow of current known as resistance Mathematically, - measured in ohms () - Resistivity of the material - length of the material - Cross section area of the material + V  i

Ohm’s Law Ohms’s Law: A voltage across a resistor is directly proportional to the current flowing through a resistor + V  i v  i Constant of proportionality between v and i is the resistance, R () v = i R Must comply with passive sign convention

Ohm’s Law Fixed resistors Wirewound type carbontype type

Ohm’s Law Variable resistors

Ohm’s Law Two extreme values of resistance: Short circuit Open circuit

Ohm’s Law Conductance: reciprocal of resistance - measured in siemens (S) Conductance: ability of an element to conduct current

Ohm’s Law + V  i Power in a Resistor Always positive Always absorbs power

Kirchhoff’s Law Network topology A branch represents a single element such as a voltage source or a resistor.

Kirchhoff’s Law Network topology A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches.

Kirchhoff’s Law Network topology A branch represents a single element such as a voltage source or a resistor. A node is the point of connection between two or more branches. A loop is any closed path in a circuit.

Kirchhoff’s Law Network topology Two or more elements are in series if they exclusively share a single node and consequently share the same current Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them 1 & 2 - parallel 10V & 4 - parallel 5 in series with (1 and 2  in parallel)

Kirchhoff’s Law 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 Mathematically,

Kirchhoff’s Law 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. Mathematically,