DC Circuit Note

                   DC Circuit

 

Electric Circuit: An electric circuit is a closed path or loop through which an electric current can flow. It typically consists of a power source (such as a battery or generator), wires or conductors to carry the current, and one or more electrical components (such as resistors, capacitors, or light bulbs) that are connected to the circuit to perform a specific function.

 

Define DC circuit: The closed path in which the direct current flows is called the DC circuit.

 The current flows in only one direction and it is mostly used in low voltage applications.

                           A simple dc circuit is:

                                   

Types of DC Circuit

The DC electric circuit is mainly classified into three groups. They are the series DC circuit, parallel DC circuit, and series and parallel DC circuit.

DC Series Circuit

A circuit in which have a DC series source, and the number of resistors are connected end to end so that the same current flow through them is called a DC series circuit. The figure below shows the simple series circuit. In the series circuit the resistors R1, R2, and R3 are connected in series across a supply voltage of V volts. The same current I is flowing through all three resistor

                        

If V1, V2, and V3 are the voltage drop across the three resistor R1, R2, and R3 respectively, then

Let R be the total resistance of the circuit then

Total resistance = Sum of the individual resistance.

In such type of circuit, all the lamps are controlled by a single switch and they cannot be controlled individually. The most common application of this circuit is for decoration purposes where a number of low voltage lamps are connected in series.

DC Parallel Circuit

A circuit which have a DC source and one end of all the resistors is joined to a common point and the other end are also joined to another common point so that current flows through them is called a DC parallel circuit.

The figure shows a simple parallel circuit. In this circuit, the three resistors R1, R2, and R3 are connected in parallel across a supply voltage of V volts. The current flowing through them is I1, I2, and I3 respectively.

       

The total current is drawn by the circuit

Let R be the total or effective resistance of the circuit, then

Reciprocal of total resistance = sum of the reciprocal of the individual resistance.

All the resistance is operated to the same voltage, therefore all of them are connected in parallel. Each of them can be controlled individually with the help of a separate switch.

DC Series-Parallel Circuit

The circuit in which a series and parallel circuits are connected in series is called a series parallel circuit. The figure below show the series-parallel circuit. In this circuit, two resistors R1 and R2 are connected in parallel with each other across terminal AB. The other three resistors R3, R4, and R6 are connected in parallel with each other across terminal BC.

The two groups of resistors RAB and RBC are connected in series with each other across the supply voltage of V volts. The total or effective resistance of the whole circuit can be determined as given below

 

Similarly Total or effective resistance of the circuit,

          

Voltage Signs

                                                                

 

 

 

 

Do you know Electrical and Electronic Engineering are Different:

                              

Let's see the difference between Electrical and Electronics Engineering :

 

Parameter	Electrical Engineering	Electronics Engineering
Definition	Electrical engineering is the branch of engineering that deals with the studies of power generation, transmission, distribution, and utilization at high voltages.	Electronics engineering is the field of engineering that deals with the utilization of electronic components such as diodes, transistors, etc. to design electronic circuits and systems.
Current flow	In electrical engineering, the electric current flows due to the movement of electrons in a conductor. Basically, electrical engineering deals with the flow of electric current in the conductors only.	In electronics engineering, the electric current is caused due to flow of electrons and holes. Electronics engineering deals with the flow of current semiconductors.
Conducting material	In electrical engineering, the conductors (or metals) such as copper, aluminum, etc. are used as the primary conducting material.	In electronics engineering, only semiconductor materials such as silicon, germanium, etc. are used.
Voltage range	Electrical engineering deals with high voltage ranges such as 220 volts in 1-phase, and 440 volts in 3-phases at the utilization end. It also uses higher voltages of the order of kV for generation, transmission, and distribution purposes.	Electronics engineering deals with the range of voltage in mV to a few volts. The typical voltage ratings used in electronics are 5V, 12V and 24V, etc.
Type of current	Alternating current (AC) is used in electrical engineering.	In electronics engineering, only direct current (DC) is used.
Power rating	In electrical engineering, the function of the electrical system is to handle a large amount of electrical power.	Electronics engineering monitors and controls low electric power.
Device size	The electrical devices and equipment are large in size and thus require more space.	Electronic devices are relatively smaller in size.
Examples of devices	Examples of electrical devices are alternators, generators, transformers, motors, circuit breakers, isolators, etc.	Examples of electronic devices are diodes, transistors, SCRs, microprocessors, integrated circuits, logic gates, etc.

 

 

 

 

                                     

Define resistance:

                                         Resistance opposes the flow of current. Resistance is different for different materials. Its unit is ohms(Ω).  Resistance is represented by R.

The formula of calculating the resistance is

                     R=V/I

                                        Where V is voltage and I is current

 Define One ohm:

                           Resistance of an object having one ampere is flowing through it when the potential different is one volt.

 

 Resistance is directly proportional to length and inversely proportional to cross section area

R ∝ L………(a)

R ∝ A………(b)

Combing two equation we get,

R ∝ L/A

R= ρ(L/A)

 

Effect of temperature upon resistance:

Effect of temperature on resistance of conductor:

The resistances of conductors vary depending on many factors such as the material of the conductor made up of, the size of the conductor, the ambient condition, etc. Temperature is also an important factor that changes the resistance of a conductor.

The effect of temperature on the resistance of the conductor is directly proportional to each other. The increase in temperature of the conductor increases its resistance and makes it difficult to flow current through it. As discussed above, the movement of free electrons creates the flow of current in the conductor.

 

Effect of temperature on resistance of semiconductor

By applying temperature to the semiconductor material, the bond strength between the atoms can be broken and this makes the electrons jump from the valence band to the conduction band and the conductivity of the semiconductor increases. Since the conductivity of a body is inversely proportional to its resistance, hence with the increase in temperature, the resistance of the semiconductor material decreases.

Effect of temperature on resistance of insulator

On the increasing temperature, the outermost electrons in the valence band vibrate and this vibration loosens the bond between the electrons and the nucleus. It provides the possibility of conduction when the valence band electrons reach the conduction band.

The increase in temperature decreases the forbidden energy gap to some extent and starts conduction. Hence, at some temperature, insulators behave as the conductor with the increase in temperature, the conductivity of the insulators increases and resistance decreases.

There are also some materials having zero resistance, which are called superconductors. The temperature at which the materials obtain zero resistance is called the critical temperature of the conductor.

 

When the relation is directly proportional, i.e, the resistance increases with the increase in temperature, it is called the positive temperature coefficient. If the resistance of the body decreases with the increase in temperature or vice-versa, the temperature coefficient is called the negative temperature coefficient.

Considering the resistance of the body at 0℃ as R_o Ω and R_t Ω at t℃.

Therefore, the change in resistance becomes

∆R = R_t – R_o       …………….. (3)

The change in resistance depends on the nature of the conductor used and from the relation given in equation (3),

∆R ∝ R_o  and ∆R ∝ t℃

Here, α is called the temperature coefficient of the resistance.

 

 

 

 

Delta to Star Conversion

 Let’s derive the equation for each impedance.

 

The given figure shows a delta network having A, B, C terminals with the impedances R₁, R₂, R₃. The equivalent star connected network with R_A, R_B & R_C where they are connected to their corresponding terminals as shown in the figure.

As mentioned earlier, the terminals A, B, C remains the same, as well as the impedance between them, must remain the same.

The total impedance between A-B in the delta network;

Similarly the impedance between terminals B-C

Similarly the impedance between A-CAccording to star network;

R_AB = R­_A + R_B

R_BC = R_B + R_C

R_AC = R­_A + R_C

Now adding equation (i), (ii) & (iii) together

Now subtract equation (i), (ii), & (iii) one by one from equation (iv)

First, Subtract (ii) from (iv)

Similarly subtracting (i) & (iii) from (iv) results in

From the derived equations for star-equivalent impedances R_A, R_B, & R_C we can conclude the relation between delta-to-star conversions as; the equivalent star impedance is equal to the product of the adjacent delta impedances with a terminal divide by the sum of all three delta impedances.

In case all three Impedances are same in a delta network, the equivalent star impedance would become

Star to Delta Conversion

Now we are going to convert the star connected impedance into delta connected impedance. Let’s derive the equations used for a star to delta conversion.

The given figure shows star connected impedance R_A, R_B & R_C. While the required delta equivalent impedance is R₁, R₂ & R₃ as shown in the figure.

In order to find the equivalent delta resistance, multiply the previous equation (v) & (vi), as well as (vi) & (vii) & (v) & (vii) together.

 Multiplying (v) & (vi)

Similarly multiplying (vi) with (vii) & (v) with (vii) 

 

Now add equation (viii), (ix) & (x) together

In order to get the individual equivalent delta impedance, we divide equation (xi) with (v), (vi) & (vii) separately such as.

Dividing (xi) with (v)

Similarly dividing equation (xi) with (vi) & (vii) separately results in

The relation between star to delta equivalent impedance is clear from the given equation. The sum of the two-product of all star-impedances divide by the star impedance of the corresponding terminal is equal to the delta impedance connected with the opposite terminal.

Simplifying the equations will lead to

In case all the star impedances are equal, the equivalent delta impedance would be;

Using the previous equation,

This equation suggests that each equivalent delta impedance is equal to 3 times the star impedance.

 

 

OHM’S LAW:

                                  According to Ohm's Law, the current flowing in a conductor is directly proportional to the potential difference across conductor.

I∝V
V

where R is constant called Resistance

                             

 

Limitations of ohm's law:

1. Ohm's law does not apply to unilateral electrical components such as diodes as well as transistors even though they only permit current just to flow in one way.

2. Voltage level will not be constant with respect to time for non-linear electrical components with properties such as capacitance, resistance, and so on, making Ohm's law problematic to apply.

3.The relation between V and I depends on the sign of V(+ or -). In other words, if I is the current for a certain V, then reversing the direction of V keeping its magnitude fixed, does not produce a current of the same magnitude as I in the opposite direction. This happens for example in the case of a diode.

4.Ohm’s law is only applicable in metallic conductors. So it won’t work in the case of non-metallic conductors.

 

Applications of Ohm’s law in Daily Life:

Ohm’s law can determine the voltage applied in a circuit, the value of resistance, and the current flowing through the circuit. With the help of the above three values, we can find the value of other factors like resistivity and many more. Some daily applications of Ohm’s law:

In fuses: In order to protect a circuit, fuses and circuit breakers are used. These are connected in series with the electrical appliances. Ohm’s law allows us to find the value of the current which could flow through the fuses. If the current value is too large, then it could damage the circuit and even lead to the explosion of the electronic device.

To know power consumption: The electrical heaters have a high-resistance metal coil that allows a certain amount of current to pass across them to provide the heat needed. Using this law, the power to be given to the heaters is determined.

To control the speed of fans: By shifting the regulator to the end from start, we can regulate the speed of the fans in our houses. By controlling the resistance via the regulator, the current flowing through the fan is managed here. We can measure the resistance, current, and thus power flowing via Ohm’s Law for any particular value of the input.

For deciding the size of resistors: Electric appliances like electric kettles and irons have a lot of resistors inside them. In order to provide the necessary amount of heat, the resistors restrict the amount of current that can flow through them. By using Ohm’s law, the size of resistors included in them is defined.

Sample Problems

Problem 1: What is the current flowing in a 75 W light bulb connected to 120 V?

Solution: 

We have given the value of power (P = 75W) and value of Voltage (V = 120V). 

We want to find the value of current I.

Using Ohm’s law,

P = IV

or

I = P / V

  = 75 / 120

  = 0.625 A.

 

Kirchhoff Current Law

KCL or Kirchhoffs current law or Kirchhoffs first law states that the total current in a closed circuit, the entering current at node is equal to the current leaving at the node or the algebraic sum of current at node in an electronic circuit is equal to zero.

                    

Kirchhoff’s Current Law

In the above diagram, the currents are denoted with i1,i2,i3,i4 ,i5and i6. According to the KCL law, the entering currents are i1,i2,i6 and the leaving currents are i3,i4 and i5. The equation can be written as

                  i1+i2+i3+ i6 =i3+i4+i5

Kirchhoff Voltage Law

KVL or Kirchhoff’s voltage law or Kirchhoffs second law states that, the algebraic sum of the voltage in a closed circuit is equal to zero or the algebraic sum of the voltage at node is equal to zero.

Numerical problem:

1. If 0.6A current flows through a resistor shown in figure. Voltage of two points of resistor is 12V. What is the resistance of the resistor?

 

Solution:

Here, Current, I = 0.6A

Potential difference or Voltage, V = 12V

Resistance, R =?

According to ohms law questions we know,

V = IR

Or, R =V / I

=12V / 0.6A

=20 Ω

Ans: 20 Ω.

2. Resistance of an electric iron 50 Ω.4.2A Current flows through the resistance. Find the voltage between two points.

Solution:

Here, Resistance, R = 50 Ω.

Current, I =4.2 A

Voltage, V =?

From Ohm’s law,

V = IR
= 4.2 × 50
= 210V

Ans: 210V.

3. Let the resistance of an electrical component remains constant while the potential difference across the two ends of the component decreases to half of its former value. What change will occur in the current through it?

Answer

According to Ohm’s law
V = IR
⇒ I=V/R ...                   (1)
Now Potential difference is decreased to half
∴ New potential difference Vʹ=V/2
Resistance remains constant
So the new current Iʹ = Vʹ/R
= (V/2)/R
= (1/2) (V/R)
= (1/2) I = I/2

Therefore, the amount of current flowing through the electrical component is reduced by half.

 

 

4.Using KVL and KCL find the branch currents in the given circuit

In loop 1, using KVL we get
2I1+2(I1−I2)=4−6