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

A

lR - measured in ohms ()

- Resistivity of the material

l - length of the material

A - Cross section area of the material

Mathematically,

+ 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

0i

0

i

vR

o

v

i

vR

Ohm’s Law

Conductance: reciprocal of resistance

v

i

R

1G - measured in siemens (S)

Conductance: ability of an element to conduct current

Ohm’s Law

Power in a Resistor

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+ V

i

Rii)iR(p 2R

v)

R

v(vp

2

Always absorbs power

Always positive

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

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N

nniMathematically,

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, 01

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