CHAPTER II

BASIC LAWS

• Ohm’s Law

• Kirchhoff’s Laws (KCL & KVL)

• To define the characteristics of the different types of sources.

• To write the mathematical expression for the voltage- current

relationship of resistors (Ohm’s Law).

• To be able to write KVL for every loop in the circuit and to solve the

KVL equations, especially for simple circuits.

• To be able to write KCL at every node in the circuit and to solve the

KCL equations, especially for simple circuits.

OBJECTIVES

Active Elements Passive Elements

R C L

• Circuit elements are either active or passive elements.

• Active elements are the energy producing elements (sources).

• Passive elements are the energy consuming (storing) elements

INTRODUCTION

Ideal Voltage Source

The ideal voltage source explicitly defines the voltage

between its terminals.

• Constant (DC) voltage source: Vs = 5 V

• Time-Varying voltage source: Vs = 10 sin(t) V

– Examples: batteries, wall outlet, function generator.

– The ideal voltage source does not provide any information about the

current flowing through it.

– The current through the voltage source is defined by the rest of the circuit

to which the source is attached.

Vs

Ideal Current Source

• The ideal current source sets the value of the current running through

it.

– Constant (DC) current source: Is = 2 A

– Time-Varying current source: Is = -3 sin(t) A

– Examples: few in real life!

• The ideal current source has known current, but unknown voltage.

• The voltage across the voltage source is defined by the rest of the

circuit to which the source is attached.

Is

I-V Relationships Graphically

i

v

Ideal Voltage Source:

Vertical line

i

v

Ideal Current Source:

Horizontal line

– Voltage sources in series can be replaced by an equivalent voltage source:

– Current sources in parallel can be replaced by an equivalent current source:

Source Combinations

i1 i2 ≡ i1+ i2

–+

–+

v1

v2

≡ –+

v1+ v2

+

-

VX+

-Element X XVVAV

A diamond-shaped symbol is used for dependent sources

Dependent Sources

• A linear dependent source is a voltage or current source that depends linearly

on some other circuit current or voltage There are voltage or current sources

depending on voltages or currents elsewhere in the circuit.

• Here, the voltage V provided by the dependent source (right) is proportional to

the voltage drop over Element X. The dependent source does not need to be

attached to the Element X in any way.

Gm Vcd

Voltage-controlled current source … I = Gm Vcd

Ai Ic

Current-controlled current source … I = Ai Ic

Rm Ic

Current-controlled voltage source … V = Rm Ic

The 4 Basic Dependent Sources

Voltage-controlled voltage source … V = Av Vcd

Av Vcd

Parameter being sensed

Constant of proportionality

Output

+

_

+

_

In the circuit shown Find Vo.

• The idea is to use the power balance

• Equation To determine the unknown voltage Vo

• Using the Power Balance

equation Vo = 18V

Example

Ohm’s Law

• Ohm discovered that voltage and current were linearly related in wires.

• That means that if you measure voltage across a wire and plot that against the

current through the wire you get a straight line in the plot.

• Ohm was able to determine that voltage and current for any fixed geometrical

structure built from conducting material satisfied a relationship:

• V is the voltage across the device, I is the current flowing through the device, R is

a constant.

• R depends upon the material from which the

device is constructed and the geometry of the

material.

R

VI

Ohm’s Law

• Any resistor has a current- voltage relationship

called Ohm’s law:

V = i R

Where,

• R is the resistance in Ω,

• i is the current in A,

• V is the voltage in V,

with reference directions as pictured.

• Since R is never negative, a resistor always

absorbs power.

• The power consumed in the

resistor is given by:

P = V I

According to Ohm’s law

I = V / R or V = IR

Therefore

P = I2R or P = V2/R

Example

If the power absorbed by Rx is

20 mW. Find Rx and Vab.

o P = 20mW = I2 Rx = 0.0022 Rx

o Rx = 5000 W

o Vab = 0.002 * Rx = 10 V

Ohm’s Law

Nodes, paths and Branches

How many nodes,

closed paths and branches?

Nodes = 3 (a , b and c )

Essential Nodes = 2 ( b, c)

Closed paths = 6

Branches = 4