Ohm’s Law:

George Simon Ohms was a German physicist invented this law which states that

voltage is directly proportional to current and proportionality constant used instead of proportional sign called  R(resistance)

Mathematical form is V=IR this is one of the most widely used formula in this course. An electronic component which cause opposition in flow of current is called resistor.It is represented by symbol “Ω”. We can also modify this formula as I=V/R -(1) or R=V/I -(2) we know that power is P=VI -(3) inserting eq.1 in eq.3 so we got P=V^2/R or P=I^2R from this thing we conclude that resistor is a passive element.In above we discuss resistance the reciprocal of resistance is conductance represented by symbol G.The unit of conductance is Siemens.

G=1/R                S=A/V

   Example:Determine the power and current of circuit

 

in this figure we have given resistance R=2kΩ and voltage V=12V we know that I=V/R=12/2K=6mA

so P=VI=(12V)(6mA)=0.072W.

Kirchhoff’s Laws:

All circuits which we discussed above are single element circuit Ohm’s law define them but in Kirchhoff’s law the circuit contain more than one element.

 

we use the above figure to understand node,loop and branch while any electric element present in the circuit is called a branch e.g(battery,inductor,capacitor,resistor),the point where two branches meet together called a node it can also be defined as the ending point of two conductors made a node in the above figure dots represents nodes. A loop is a closed path in which a node is not repeated more than once in above circuit R1,V2,R4 and i1 represents a loop. In electrical engineering Kirchhoff’s laws are very important there are two laws

1.Kirchhoff’s Current Law:

the sum of all currents entering a node and sum of all currents leaving a node are equal

Example:Find the unknown current

 

Node 1:

I1=61mA+22mA

Node 2:

I4=I1+I6

Node 3:

  61mA+I5=I4+4mA

Node 4:

22mA+3mA=I5

Node 5:

I6+4mA=3mA

I6= -1mA, I5= 25mA, I1= 83mA

2.Kirchhoff’s Voltage Law:

the algebraic sum of all voltages in a loop equal to zero

Example:Find unknown voltage Vr1=5V and Vr3=5v

 

-10+Vr1-10+Vr2-10+Vr3=0

Vr3=20V

Voltage Distribution Rule (VDR):

In a series circuit all electronic components are connected in single path next to each other. In a series circuit current remain same figure given above is a series circuit.

Series  circuit equation                                                         Rt=R1+R2+……Rn

the figure given above is a series circuit with a multiple source in which we have value of S1=5V but current is same for whole circuit so equation is                                         –v+5V+R2.i=0

to calculate i from this equation is                                    i=v – 5V / R2

 

This is a single source series circuit in which voltage across R1 and R2 is unknown first we write it’s KVL equation

-v+Vr1+Vr2=0

v=Vr1+Vr2       -(1)

v=I.R1+I.R2       -(2)

to calculate i we can simplify this equation            I= v / R1 + R2   -(3)

now applying Ohm’s law for R1                                      Vr1=I.R1

inserting value of I in above eq. so got                          Vr1=(v).R1/(R1+R2)  -(4)

same for R2                                                                         Vr2=R2.(v)/(R1+R2)  -(5)

inserting eq 4,5 in eq 1

v=R1.(v)/(R1+R2)+R2.(v)/(R1+R2)

Current Distribution Rule (CDR):

In parallel circuits electric components are connected side-by-side and they have same voltage across each component.Our houses electrical installations are also in parallel connections.Parallel equation is                    1/Rt=1/R1+1/R2+……1/Rn

Story “In series combination if one component stop working it will effect the whole circuit and current stops flowing but in parallel circuit if any element stops working this thing will not effect the other one’s and current keeps flowing”

 

This is a parallel circuit let assume that voltage V across R1 and R2 so it’s KCL eq. is

I=I1+I2      -(1)

I=V / R1 + V / R2     -(2)

I=V / (R1+R2)

I= V / Rt -(3)

so total resistance in parallel comb. is                   Rt= 1 / R1 + 1/R2

Rt= R1.R2 / R1 + R2   -(4)

applying eq.4 in ohm’s law V=I.Rt

V=(R1.R2) / (R1 + R2) . I

so I1 for the given figure is                                        I1=V/R1

I1= R2 / (R1+R2) . I

for I2 it is                                                                      I2=V/R2

I2= R1 / (R1+R2) . I

Series and parallel resistors combinations:

In this topic we have to find equivalent resistance let’s take an example

first we add 6k and 3k so our circuit will look like

 

so 18k and 9k are in parallel so simplify them

 

now it’s a simple series combination so there addition is 22kΩ.

 

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