Chapter 2: Basic laws

ECE 1311: Electric Circuits

Basic Law Overview

Ideal sources – series and parallel

Ohm’s law

Definitions – open circuits, short circuits, conductance,

nodes, branches, loops

Kirchhoff's law

Voltage divider and series resistors

Current divider and parallel resistors

Wye-Delta transformations

Ideal Voltage Source

Ideal voltage source in series can be added

Ideal voltage source in parallel = NO GOOD

Recall: ideal voltage source guarantee the voltage between

two terminals is at the specified potential (voltage)

BOOM

Ideal Current Source

Ideal current source cannot be connected in series

Ideal current source in parallel can be added

Recall: ideal current guarantee the current flowing through

source is at the specified value

Recall: Current entering a circuit must be equal to the

current leaving the circuit

BOOM

Resistance

All material resist the flow of current given by R • R = resistance of an element in ohms

• p = resistivity of material in ohm-meters

• l = length of material in meters

• A = cross sectional area of material in meter2

A

lR

Ohm’s Law (1)

Ohm’s law states that the voltage across a resistor is directly

proportional to the current flowing through the resistor.

Only material with linear relationship satisfy Ohm’s law

(note the PSC)

iRv

Ohm’s Law (2) Two extreme possible values of R: 0 (zero) and (infinite) are

related with two basic circuit concepts: short circuit and open

circuit.

Conductance is the ability of an element to conduct electric current; it is the reciprocal of resistance R and is measured in mhos or siemens.

The power dissipated by a resistor:

Power absorbed by R is always positive

v

i

RG

1

R

vRivip

22

Practice 2.1

Short circuit

An element (or wire) with R = 0 is called a short circuit

An ideal voltage source with V = 0 is equivalent to a short

circuit

Since v = iR and R = 0, v = 0 regardless of i

Recall: cannot connect voltage source to a short circuit

Open circuit

An element with R = is called the open circuit

Often represented by a wire with an open connection

An ideal current source I = 0A is also equivalent to an open

circuit

Recall: cannot connect current source to an open circuit

Formalization

For this course, networks and circuits will be used

interchangeably

Networks are composed of nodes, branches and loops

Nodes, Branches and Loops

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.

A network with b branches, n nodes, and l independent

loops will satisfy the fundamental theorem of network

topology:

1 nlb

Practice 2.2

How many branches, nodes and independent loops are there?

Practice 2.3

How many branches, nodes and loops are there?

Overview on Kirchhoff’s Law

It’s the foundation of circuit analysis

There are two - Kirchhoff’s current law (KCL) and

Kirchhoff’s voltage law (KVL)

It tell us how the voltage and current are related within a

circuit element are related

Kirchhoff’s Current Law (1)

Kirchhoff’s current law (KCL) states that the algebraic

sum of currents entering a node (or a closed

boundary) is zero.

i.e. the sum entering a node is equal to the sum leaving a

node – based on the law on conservation charge

Kirchhoff’s Current Law (2)

KCL also apply at the boundary

Practice 2.4

Given that essential node is the point between 3 or more

branches,

Kirchhoff’s Voltage Law (1)

Kirchhoff’s voltage law (KVL) states that the algebraic

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

Based on the conservation of energy

Practice 2.5

Practice 2.6

Apply KVL to find the value I

Summary on Ohm’s Law, KCL and KVL

Ohm’s Law

KCL

KVL

These law alone are sufficient to analyze many circuits

0

0

n

n

V

I

iRv

Practice 2.7

Find v2, v6 and vI

Practice 2.8

Find i0 and v0

Practice 2.9

Resistor Circuit Overview

Resistors in series

Resistors in parallel

Voltage dividers

Current dividers

Wye-Delta transformation

Resistors in series

Resistors in Parallel (1)

Resistors in Parallel (2)

Voltage Divider

Current Divider

Resistor Network

Knowing equivalent and parallel equivalents of resistors is

not enough

Wye-Delta Transformation (1)

)(1

cba

cb

RRR

RRR

)(2

cba

ac

RRR

RRR

)(3

cba

ba

RRR

RRR

1

133221

R

RRRRRRRa

2

133221

R

RRRRRRRb

3

133221

R

RRRRRRRc

Delta -> Y Y -> Delta

Wye-Delta Transformation (2)

Practice 2.10

Practice 2.11

Practice 2.12