Basic Laws

FUNDAMENTAL LAWS THAT GOVERN ELECTRIC CIRCUITS

Introduction:

Fundamental laws that govern electric circuits:

  • Ohm’s Law
  • Kirchoff’s Law

These laws form the foundation upon which electric circuit analysis is built.

Common techniques in circuit analysis and design:

  • Combining resistors in series and parallel.
  • Voltage and current divisions.
  • wye to delta and delta to wye transformations

THESE TECHNIQUES ARE RESTRICTED TO RESISTIVE CIRCUITS.


 

What is Ohms law?

Relationship between current and voltage with in a circuit element.

The voltage across an element is directly proportional to the current flowing through it      → v α i 

Thus:: v=iR   and R= v/i

where:

  • R is called resistor
  • Has the ability to resist the flow of electric current
  • Measured in Ohms (Ω)

 

Ohms_Law

NOTE THAT:

  •  RESISTOR HAS NO POLARITY
  • THE RESISTANCE VARIES FROM  0 TO ∞
  • ONLY LINEAR RESISTORS OBEY THE LAW

 

Conductance

Conductance is the extrinsic property. This means that conductance is the property of an object dependent of its amount/mass or physical shape and size.

  • The unit used is mho or siomens (S).
  • It has the ability to conduct electric current

image57

Power

R and G are positive quantities, thus power is always positive (+)  such that R absorbs power.

images

 

EXAMPLES:

Untitled

Solutions:

For voltage:

v=iR

v = (2*10^-3)(10*10^3)

v = 20 volts

For Conductance:

G=i/R

=1/10*10^3

G=1*10^-4

For Power:

P=t^2R

=v^2/R

=(2*10^-3)^2 (10*10^3)

=0.04 w

=40mW

=(20)^2/10*10^3

P=0.04 w

Untitled

Solution:

(a) i = 3/100 = 30 mA

(b) i = 3/150 = 20 mA

 



 

NODES, BRANCHES AND LOOPS

Elements of circuit can be interconnected in several ways and we need to understand the basic topology of this.

A branch represents a single element such as voltage source or a current source or a resistor.

branch-node-loop1.jpg

A node is the point of connection between two or more branches.

Node is indicated by dot sign. When a short circuit has two nodes it actually becomes one node. If we redraw the first circuit as it has two common points shown in black color filled.

branch-node-loops-nn1.jpg

After redrawing the circuit  becomes as below circuit. It shows three nodes a, b, c.

branch-node-loops1.jpg

A loop is any closed path in a circuit.branch-node-loops-nnkkll1 (1).jpg

 

EXAMPLES:

Untitled

Solutions

Re draw the given figure:

Untitled

Answer:

5 branches

  • 1 voltage source
  • 1 current source
  • 3 resistors

3 nodes

  • a
  • b
  • c

Another example:

Untitled

There were 7 branches, 4 nodes, and 10 loops all in all.

 



Kirchoffs Circuit Law

Kirchhoff’s First Law

The law states that at any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.

Examples:

  • Given the following circuit, write the equation for currents.

yeye2

 

  • Current in a close boundary.

yeye3


  • Use KCL to obtain currents i1, i2, and i3 in the circuits.

yeye4

Solutions:

A= 1A+i1=2A+10A

i1=12A-1A

i1=11A

B= 3A+2A=1A+i2

5A=1A+i2

i2=4A

C= i3+10A=11A

i3=11A-10A

i3=1A

Kirchhoff’s Second Law

This animation shows a multiple loop circuit which illustrates Kirchhoff’s second law which states that the sum of the potential differences as you go around the loop is zero.


Kirchoff’s Voltage Law (KVL)

  • Applied to a loop in a circuit.
  • According to KVL ( the algebraic sum of voltage rises and drops in a loop is zer0. 

KVL

Examples:

Untitled

Solution:

+20+25-10-v1=0

V1=35v

+10-15+v2=0

v2=-10+15

v2=5V

+v1-5-v3=0

35-5-v3=0

v3=30V

Another example:

Untitled

Solution:

+10v+12v+6v-v1-v1=0

28v-2V1=0

28V/2=2V1/2

V1= 14V

+V2-12V-10V=0

+12V-22V=0

V2= 22V

Untitled

Solution: 

Power= iv = i²R = v²/ R

V 5Ω = 5i

45-10i + 3vo – 5i =0

vo = 10i

45-Vo + 3vo -5i = 0

i = Vo/10

45-Vo +3vo -5 (Vo/10) = 0



Summary:

There are two basic laws that were introduced to us.

The first law is the “Ohms Law” which states that the voltage across a resistor is directly proportional to the current flowing to through the resistor, represented by and equation V=IR. This law deals with the resistance (R).

An element with R=0 is called “Short Circuit” which means the resistance is almost or approaching to zero. If the resistance of the circuit element is approaching to infinity it is called “Open Circuit” this means that the current cannot flow because the path has been interrupted.

The second law is the “Kirchhoff’s Law“, which is divided into two parts, the “Kirchhoff’s Current Law“, which is the sum of the currents entering a node is equal to the sum of the current leaving the node, and the “Kirchhoff’s Voltage Law”, which states that the sum of voltage drop around the loop is equal to the sum of the voltage rises in the same loop.

There are three elements in a circuit.

The first element is the “Branch”; it represents a single element (Volt source or Resistor). Second is the “Node”, it is the point of connection between two or more branches. And lastly the “Loops“, which is any closed path in a circuit.

Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference across those two points. It means that more the resistance lesser current would flow. I=V/R This would apply to any component of a circuit. For example conductors would increase the current flow and the inductors would decrease it.

 

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