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BASIC LAWS

Ohms Law

Kirchhoffs Law

Series resistors & voltage division

Parallel resistors & current division

Y -

transformation

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Ohms 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

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Ohms Law

Ohmss Law: A voltage across a resistor is directly proportional tothe 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

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Ohms Law

Fixed resistors

Wirewound type

carbontype type

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Ohms Law

Variable resistors

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Ohms Law

Two extreme values of resistance:

Short circuit

Open circuit

0i

0

i

vR

ov

ivR

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Ohms Law

Conductance: reciprocal of resistance

v

i

R

1G - measured in siemens (S)

Conductance: ability of an element to conduct current

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Ohms Law

Power in a Resistor

vip

+ V

i

Rii)iR(p 2R

v)

R

v(vp

2

Always absorbs power

Always positive

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Kirchhoffs Law

Network topology

A branch represents a single element such as avoltage source or a resistor.

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Kirchhoffs Law

Network topology

A branch represents a single element such as avoltage source or a resistor.

A node is the point of connection between two

or more branches.

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Kirchhoffs Law

Network topology

A branch represents a single element such as avoltage 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.

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Kirchhoffs Law

Network topology

Two or more elements are inseries if they exclusivelyshare a single node and consequently share the samecurrent

Two or more elements are inparallel if they areconnected to the same two nodes and consequentlyhave the same voltage across them

1 & 2 - parallel

10V & 4 - parallel

5 in series with (1 and 2 in parallel)

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Kirchhoffs Law

Kirchhoffs Current Law (KCL)

Kirchhoffs current law (KCL) states that the algebraic sum

of currents entering a node (or a closed boundary) is zero

0

1

N

n

niMathematically,

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Kirchhoffs Law

Kirchhoffs Voltage Law (KVL)

Kirchhoffs voltage law (KVL) states that the algebraic sum

of all voltages around a closed path (or loop) is zero.

Mathematically, 01

M

m

nv