Circuit theory basics

BASICS OF CIRCUIT
THEORY
Compiled By

Shruti Bhatnagar Dasgupta

CIRCUIT ELEMENTS
 In circuits, we think about basic circuit elements that are the
“building blocks” of our circuits. This is similar to what we do
in Chemistry with chemical elements like oxygen or nitrogen.
 A circuit element cannot be broken down or subdivided
into other circuit elements.
 A circuit element can be defined in terms of the behavior
of the voltage and current at its terminals.

THE 5 BASIC CIRCUIT
ELEMENTS
There are 5 basic circuit elements:
1.

Voltage sources

2.

Current sources

3.

Resistors

4.

Inductors

5.

Capacitors

VO LTAG E S O U RC E S
 A voltage source is a two-terminal circuit element that maintains a
voltage across its terminals.
 The value of the voltage is the defining characteristic of a voltage
source.
 Any value of the current can go through the voltage source, in any
direction. The current can also be zero. The voltage source is not
concerned about the current. It focuses only about voltage.

VO LTAG E S O U R C E S – 2 K I N D S
There are 2 kinds of voltage sources:
1.

Independent voltage sources

2.

Dependent voltage sources, of which there are 2 forms:
i.
ii.

Voltage-dependent voltage sources
Current-dependent voltage sources

VO LTAG E S O U R C E S –
S C H E M AT I C S Y M B O L F O R
INDEPENDENT SOURCES
The schematic symbol that we
use for independent voltage
sources is shown here.

+
vS=
#[V]

-

Independent
voltage
source

This is intended to indicate that the schematic symbol can be labeled either with a variable,
like vS, or a value, with some number, and units. An example might be 1.5[V]. It could also
be labeled with both.

VO LTAG E S O U R C E S
– S C H E M AT I C
SYMBOLS FOR DEPENDENT
VO LTAG E S O U R C E S
The schematic symbols that we use for dependent voltage sources
are shown here, of which there are 2 forms:
i.
ii.

vS =

m vX

+
-

Voltagedependent
voltage
source

vS =
r iX

+
-

Currentdependent
voltage
source

S C H E M AT I C S Y M B O L S F O R
D E P E N D E N T VO LTAG E S O U R C E S
The schematic symbols that we use for dependent voltage sources are
shown here, of which there are 2 forms:
i.
ii.
The symbol m is the coefficient of the voltage vX. It
is dimensionless. For example, it might be 4.3 vX.
The vX is a voltage somewhere in the circuit.

vS =
m vX

+
-

Voltagedependent
voltage
source

The symbol r is the coefficient of the current iX. It has
dimensions of [voltage/current]. For example, it might
be 4.3[V/A] iX. The iX is a current somewhere in the
circuit.

vS =

r iX

+
-

Currentdependent
voltage
source

C U R R E N T S O U RC E S
 A current source is a two-terminal circuit element that maintains a
current through its terminals.
 The value of the current is the defining characteristic of the current

source.
 Any voltage can be across the current source, in either polarity. It can
also be zero. The current source does not “care about” voltage. It
“cares” only about current.

C U R R E N T S O U RC E S - I D E A L
 A current source maintains a current through its terminals no matter
what you connect to those terminals.
 While there will be devices that reasonably model current
sources, these devices are not as familiar as batteries.

C U R R E N T S O U RC E S – 2 K I N D S
There are 2 kinds of current sources:
1.

Independent current sources

2.

Dependent current sources, of which there are 2 forms:

i.
ii.

Voltage-dependent current sources
Current-dependent current sources

C U R R E N T S O U R C E S – S C H E M AT I C
SYMBOL FOR INDEPENDENT
SOURCES

The schematic symbols that we use for current
sources are shown here.

iS=
#[A]

Independent
current
source

This is intended to indicate that the schematic symbol can be labeled
either with a variable, like iS, or a value, with some number, and units.
An example might be 0.2[A]. It could also be labeled with both.

S C H E M AT I C S Y M B O L S F O R D E P E N D E N T
CURRENT SOURCES
The schematic symbols that we use for dependent current sources are shown
here, of which there are 2 forms:
i.
ii.

iS=
g vX

Voltagedependent
current
source

iS=
b iX

Currentdependent
current
source

S C H E M AT I C S Y M B O L S F O R D E P E N D E N T
CURRENT SOURCES
The schematic symbols that we use for dependent current sources are
shown here, of which there are 2 forms:
i.
ii.
The symbol g is the coefficient of the voltage vX. It
has dimensions of [current/voltage]. For example, it
might be 16[A/V] vX. The vX is a voltage somewhere
in the circuit.

iS=
g vX

Voltagedependent
current
source

The symbol b is the coefficient of the current iX. It is dimensionless.
For example, it might be 53.7 iX. The iX is a current somewhere in the
circuit.

iS=

b iX

Currentdependent
current
source

Voltage and Current Sources
•

Real Voltage Source and Real Current Source
•

In “real” sources there is always some energy loss.

i

i

+
Vs

-

R
V

+

V

Is

-

R

LINEAR COMPONENTS
 Resistor, Capacitor, Inductor, and Transformer
I
+

V= I.R
i

V
R

-

v

i

L

+

i = C. dv
dt

v
C

-

v = L. di
dt

+

-

LINEARITY’S PRINCIPLE
f( α  x1  β  x 2 )  α  f(x 1 )  β  f(x 2 )

Linearity = Scaling + Superposition

Scaling : f ( k  x )  k  f ( x )
Superposit ion : f ( x1  x 2 )  f ( x1 )  f ( x 2 )

RESISTORS
 A resistor is a two terminal circuit element that has a constant ratio of
the voltage across its terminals to the current through its terminals.
 The value of the ratio of voltage to current is the defining characteristic
of the resistor.

R

+

where R is the resistance.

iR

v

-

OHM’S LAW
 The voltage across a conductor is proportional to the current
flowing through it:V= I.R

 The Proportionality constant is called Resistance (R).

CAPACITOR
 A capacitor or a condenser is a passive two-terminal electrical component used
to store energy electrostatically in an electric field.
 The forms of practical capacitors contain at least two electrical conductors
(plates) separated by a dielectric (insulator). The conductors can be thin films of
metal, aluminum foil or disks, etc. The 'non-conducting' dielectric acts to increase
the capacitor's charge capacity. A dielectric can be glass, ceramic, plastic
film, air, paper, mica, etc.
 Unlike a resistor, a capacitor does not dissipate energy. Instead, a capacitor
stores energy in the form of an electrostatic field between its plates.

 Its symbols are:
+
A capacitor

A Polarised

A Variable

Capacitor

Capacitor

An ideal capacitor is wholly characterized by a constant capacitance C, defined as
the ratio of charge ±Q on each conductor to the voltage V between them:
C= Q/V

INDUCTORS
 An inductor or coil or reactor, is a passive two-terminal electrical
component which resists changes in electric current passing through it.
 It consists of a conductor such as a wire, usually wound into a coil.
 When a current flows through it, energy is stored temporarily in a
magnetic field in the coil. When the current flowing through an inductor
changes, the time-varying magnetic field induces a voltage in the
conductor,

according

to

Faraday’s

law

of

electromagnetic

induction, which opposes the change in current that created it.

 Its symbol is:

 inductance is determined by how much magnetic flux Φ through
the circuit is created by a given current (i)
 L = Φ/i

Circuit theory basics

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