: Networks : Basics

Passive Elements/ Basic elements of a network:

R= Resistance; unit is Ω  --> read as Ohm 

L = Inductance; unit is H --> read as Henry

C= Capacitance; unit is F --> read as Farad

Steady State Analysis

 V= I R

V = I XL

V = I XC 

Transient analysis 

V = i(t) R

V =L di(t)/dt

V =(1/C) ∫ i(t) dt

When do you say that two or more elements are in series: starting from point A, if the current does not split and reaches point B. Then all the elements in between point A and B are in Series.

When do you say that two or more elements are in parallel: starting from point A, if the current splits and reaches point B. Then all the elements in between point A and B are in Parallel.

SERIES:

Resistance: 

When two or more resistors are connected in series, then equivalent (overall value) is

Req = R1 + R2 + R3 + ...

Inductance: 

When two or more inductors are connected in series, then equivalent (overall value) is

Leq = L1 + L2 + L3 + ...

Capacitance: 

When two or more capacitors are connected in series, then equivalent (overall value) is

(1/Ceq) = (1/C1)+ (1/C2)+(1/C3)+ ...

PARALLEL:

Resistance: 

When two or more resistors are connected in series, then equivalent (overall value) is

(1/Req) = (1/R1)+ (1/R2)+(1/R3)+ ...

Inductance: 

When two or more inductors are connected in series, then equivalent (overall value) is

(1/Leq) = (1/L1)+ (1/L2)+(1/L3)+ ...

Capacitance: 

When two or more capacitors are connected in series, then equivalent (overall value) is

Ceq = C1 + C2 + C3 + ...

Now using above formulae, we shall calculate the equivalent element value.

(a) RAB  = 100 + 1K = 100 + 1000 = 1100 = 1.1 kΩ

(b) LAB  = 100m + 100µ = 100m + 0.1m  = 100.1mH

(c) CAB  = ?; 

(1/CAB )= (1/100µ)+(1/1µ) = 101µ/ (100µ x 1µ)

=>

CAB = (100µ x 1µ)/101µ = 100µ /101 = 0.99 µF

(d)  RAB  = ?; 

(1/RAB )= (1/10)+(1/4.7k) = (10+4.7k)/ (10 x 4.7k)

=>

RAB = (10 x 4.7k)/(10+4.7k) = 47k /4710 = 47000/4710 = 9.98 kΩ

(e)  LAB  = ?; 

(1/LAB )= (1/50m)+(1/1m) = (50m+1m)/ (50m x 1m)

=>

LAB = (50m x 1m)/(50m+1m) = 50m /51 = 0.98 mH

(f) CAB  = 100nF + 1µF = 0.1µF + 1µF = 1.1 µF

Below are the Special Models that are neither series nor parallel completely:

Solve the below problems based on above knowledge:

Sources are of two types: 

Voltage and Current Source

Various categorization of sources are as below:

Ideal and Non-ideal (practical)

Dependent and Independent

Non-ideal Sources (Practical Sources)

Ideally sources can not exist. So, they do have some internal resistance. The series or parallel resistance appearing next to the source is the same that we observe. 

Dependent Sources

Circle shape = Independent Source (above discussed are independent sources; only two types)

Diamond shape = Dependent source (below discussed are dependent sources; FOUR types)

Voltage Sources -Series only: parallel combination is not valid

Solutions to above questions:

Current Sources- Parallel only: series combination is not valid

Solutions to above problems:

Network = Circuit = elements connected.

Let us take 10Ω as LOAD (context here is point of observation).

S.C:

Short Circuit (S.C) -->R= 0 

So, if R=0, then V= I R = 0

i.e., S.C<--> V=0 <--> R=0

Open Circuit(O.C)--> R= ∞ 

So, if R=∞, then V= I R = ∞ ; But this is undefined value; Hence V= open terminal equivalent voltage

i.e., O.C <--> V≠0 (mostly) <--> R= ∞