Circuit analysis Tutorial

Voltage, Current & Resistance

In electronics we are dealing with voltage, current and resistance in circuits.

Voltage

Voltage is the electrical force, that causes current to flow in a circuit. It is measured in VOLTS .

Electrical Current

Current is the movement of electrical charge - the flow of electrons other charged particles through the electronic circuit. The direction of a current is opposite to electrons flow direction. Current is measured in AMPERES (AMPS, A ).

Resistance

Resistance causes an opposition to the flow of electricity in a circuit. It is used to control the amount of voltage and/or amperage in a circuit. It is measured in OHMS.

Electrical symbols

Electronic component are classed into either being Passive devices or Active devices. A Passive Device is one that contributes no power gain to a circuit or system. Examples are Resistors, Light Bulb, Electrical Heaters. Active Devices are components that are capable of generating voltages or currents. Examples are Batteries and other Electrical Curent & Voltage Sources.


By using schematics symbols we can represent real-life devices.


Resistance -This is a resistance, measured in units ohms ohms, . Most often it will be a resistor.






This is a source of emf (electromotive force) or voltage source, with a voltage of , measured in units of volts, V. The most common source you will see will be a battery. However, batteries are really not resistance-free. We can model this case by putting a 'resistor' in the circuit which has the same resistance as the batterys would have.


This is a current source, with a current of , measured in units of amperes , A. Current source is ideal model of electrical power source. The internal current source resistance is infinity. We can model real life battery by putting a 'resistor' in parallel with curent source.

Ohm’s law

Ohm's law is the main basic electrical law and defines the resistance of a device to the flow of electrons.

There are three different notations of Ohm’s law

1. Unknown current

2. Unknown voltage

3. Unknown resistance


(Most people can remember a picture easier than a mathematical formula. By knowing any two values you can figure out the third. Simply put your finger over the portion of the symbol you are trying to figure out and you have your formula)


1.


2.





3.

Superposition theorem

In a network with multiple voltage sources, the current in any branch is the sum of the currents which would flow in that branch due to each voltage source acting alone with all other voltage sources replaced by their internal impedances.


The goal of folowing text is to check superposition theorem.


Step 1. Construct following circuit using Circuit Magic then run Node Voltage Analysis. (popular circuits analysis technique). You can alsocalculate currents using other techniques




Electrical scheme


Inital variables
R2=10Ohms; R1=10Ohms; R3=10Ohms;
E1=3V; E3=4V; Solution
V1·G11=I11G11=1/R1+1/R2+1/R3=0,3
I11=-E1/R1-E3/R3=-0,70,3V1=-0,7
V1=-2,3333
V2=0
I1=(V1-V2+E1)/R1=0,0666667
I2=(V1-V2)/R2=-0,233333
I3=(V1-V2+E3)/R3=0,166667

These values are used to check currents determined from superposition theorem

Step 2. Remove a voltage source from the third branch then run Node Voltage Analysis.


Electrical scheme
Inital variables
R2=10Ohms; R1=10Ohms; R3=10Ohms;
E1=3V;
Solution
V1·G11=I11G11=1/R1+1/R2+1/R3=0,3
I11=-E1/R1=-0,30,3V1=-0,3
V1=-1
V2=0
I1(1)=(V1-V2+E1)/R1=0,2
I2(1)=(V1-V2)/R2=-0,1
I3(1)=(V1-V2)/R3=-0,1


These values are used to determine current from superposition theorem.

Step 3. Remove a voltage source from the first branch then run Node Voltage Analysis.


Electrical scheme
Inital variables
R2=10Ohms; R1=10Ohms; R3=10Ohms;
E3=4V;
Solution
V1·G11=I11G11=1/R1+1/R2+1/R3=0,3
I11=-E3/R3=-0,40,3V1=-0,4
V1=-1,3333
V2=0
I1(2)=(V1-V2)/R1=-0,133333
I2(2)=(V1-V2)/R2=-0,133333
I3(2)=(V1-V2+E3)/R3=0,266667


Superposition theorem checking


I1=I1(1)+I1(2)=0,2-0,133333=0,0666666
I2=I2(1)+I2(2)=-0,1-0,133333=-0,233333
I3=I3(1)+I3(2)==-0,1+0,266667=0,166667

Kirchhoff's Current Law (KCL)

KCL states that the algebraic sum of the currents in all the branches which converge in a common node is equal to zero


SIin = SIout

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law states that the algebraic sum of the voltages between successive nodes in a closed path in the network is equal to zero.

SE = SIR

Solution using Kirchhoff’s Voltage and current laws

Steps to solve circuit by Kirchhoff’s Laws.

1. Construct circuit with circuit magic schematics editor.



Circuit sample from circuit magic.




2. Construct loops. (See “creating loop” section in user guide) Number of loops (and number of Kirhhoff’s Voltage laws equations) can be determined using following formula. Loop can not include branches with current sources. Due current sources resistance equal infinity.


Loop Number = Branch Number –(Nodes Number –1) – Current sources Number


3. Select Analyze->Solve by Kirhhoff’s laws menu item
In dialog box press OK button. if no warning shown.
Read solution.




Solution example from circuit magic.


Writing Kirchhoff current law for 3-1 nodes


(Note number of Kirchhoff current laws equations equal Nodes Number –1)


(Node 1)J1+I3+I4+I7=0


(Node 2)-J1+I2-I4=0


Wrining Kirchoff voltage law for 5-1-(3-1) loops


(Loop1) I3·R3-I7·R5=-E2


(Loop2) I2·R2-I7·R5+I4·R4=E1-E2


Linear equations


I3+I4+I7=-2


I2-I4=2


10I3-10I7=-10


11I2+10I4-10I7=-7


Equations solution


I1=2


I2=0,692


I3=-0,846


I4=-1,308





I7=0,154

Resistors in Series & Resistors in Parallel

A series circuit is one with all the loads in a row. Like links in a chain. There is only one path for the electricity to flow.





A parallel circuit is one that has two or more paths for the electricity to flow. In other words, the loads are parallel to each other.