Electric current:

Current can be defined as the flow of electric charge through a conductor, typically in the form of electrons moving through a wire.it is measured in amperes (A)Current can be categorized into two types: direct current (DC) and alternating current (AC)

Alternating current (AC):

An alternating current is a type of current whose magnitudes and direction change over time is called alternating current.

An alternating current is a bidirectional electric current, so the flow of charge is not in the same direction. The direction and magnitude of alternating current are alternatives.

Direct current (DC):

Direct current is a type of current whose magnitude and direction are constant for time is called direct current.

Direct current is an electric current that is uni-directional, so the flow of charge is always in the same direction. As opposed to alternating current, the direction and magnitude of the direction of direct current do not change.

Comparison between Alternating Current and Direct current.

Alternating Current(AC)	Direct Current(DC)
The magnitude and direction of alternating current change over time.	The magnitude and direction of direct current do not change over time.
Alternating current can be produced by the generator.	Direct current can be produced by battery, solar, and cell
Alternating current is widely used in homes, businesses, and industries.	Direct current is widely used in electronic devices and low-voltage systems.

Resistance(R):

Resistance is an electronic component that opposes the flow of electric current in the circuit. Resistances are used in electronic circuits to adjust the current and voltage. The SI unit of electrical resistance is the ohm, and it is represented by Ω.

The Symbol of Electrical Resistance:

Types of Resistance:

Resistances are broadly categorized into two types, and these are fixed resistance and Variable resistance.

Fixed Resistance:

Fixed resistance can be defined as the resistance whose value does not change with any change in temperature or voltage. These resistances are available in different shapes and sizes

Variable Resistance: 

Variable resistance can be defined as the resistance whose value changes with any change in temperature or voltage.

Resistor Color Code 

The values of resistors are determined by the color band marked on the resistor body. The color code marking system has been adopted by the Electronics Industries Association (EIA) and the United States Armed Forces and is recognized throughout the world.

Resistor Color Code Table

    Fig: color code table of Resistor

Numerical 1:  Find the resistance of the given resistor

Tolerance = Value of Resistor × Value of Tolerance Band

                  = 22000 Ω ⨯ 10 % = 2200 Ω

This means that the 22000 Ω resistors with a tolerance value of 2200 Ω could range from the actual value of as much as 19800 Ω to as little as 24200 Ω. 

Numerical 2: Find the value of the carbon resistor with color bands Yellow, Violet, Brown, and Gold.

Solution

Resistance value = 47×10 Ω

Tolerance = Value of Resistor × Value of Tolerance Band

                = 470 Ω x5% = 23.5 Ω

This means that the 23.5 Ω resistors with a tolerance value of 23.5 Ω could range from the actual value of as much as 446.5 Ω to as little as 493.5 Ω

Numerical 3:  Find the value of the carbon resistor with color bands Red, Yellow, and Gold.

Law of Resistance:  

Fig: The Law of Resistance

Let us consider a conductor of length (l) and cross-section area (A), shown in the above diagram. The law of resistance states that material resistance depends upon the following factors: law of resistance.

• The resistance of a conductor is directly proportional to the length of the conductor. It means that if the length of a conductor increases then the values of resistance also increase. Mathematically it is given as

R ∝ L…………………. (eq. 1)

• The resistance of the conductor is inversely proportional to the cross-sectional area of the conductor. It means that if the conductor’s cross-sectional area increases, the resistance value will decrease. Mathematically, it is given as

R ∝ l / A ………..(eq. 2)

• The resistance of the conductor depends upon the nature of the conductor. Now, combining equations 1 and 2, we have

Where p  is called Rho. It is called constant and known as the resistivity or specific resistance of a material.

Unit of resistivity: 

       We know that from the law of resistance.

Thus, the unit of resistivity is (meter–ohm) or (ohm-meter)

Combination of Resistors:

Resistances are used in various combinations. There are two main methods of arranging the resistors in different combinations.

1. Resistors are in a series combination
2. Resistors are in a parallel combination

Resistors are in a series combination:

Two or more resistances are said to be in a series combination when they are connected end to end and the same amount of current flows through each resistance.

The equivalent or total resistance of any number of resistances (R1, R2, R3,……..) connected in a series combination is given as

R _equ = R₁+R₂+R₃+ ……..

Let us consider two resistances R₁ and R ₂   connected in series with each other with the corresponding voltage source V₁ and V₂ in a circuit shown below.

The equivalent potential difference is equal to the sum of all individual potential differences across each resistor, and the current following through each resistor is the same i.e. I = i₁=i₂

Applying Ohm’s law to all individual resistor

V₁=IR₁ ………………….. (1)

V₂=IR₂ …………………. (2)

V= IR …………………… (3)

Now applying KVL in the above circuit

V= V1+V2

Or     IR = IR₁+IR₂

Or    I R =I (R₁+R₂)

Or     I R =I (R₁+R₂)

Or       R_eqv = R₁+R₂ ………………… (4)

Properties of a series circuit

• An equal amount of current travels through each resistance.
• Supply voltage V is equal to the sum of all individual voltage drops across the resistors. i.e. V= V₁+V₂+V₃+…….V_N
• Net electrical resistance is equal to the sum of an individual’s resistance.

Resistors are in parallel  combination

Two or more resistances are said to be connected in parallel if their components are connected across the common point, and offer multiple pathways for the current.

In a parallel combination of resistance, the reciprocal of the total resistance is the sum of the reciprocal of individual resistance.

Let us consider two resistances R₁ and R₂ connected in parallel with each other with corresponding voltages v₁ and V₂ in a circuit shown below the diagram.

Resistance in Parallel Combination

Here the electric current following through each resistor is different therefore, the equivalent current following through the circuit is

I_{eqv =}  I₁ + I₂ …………………………….(1)

Applying Ohm’s law to the individual resistor as

A

Application of Resistance:

Some common applications of resistance are given below.

1. Electric Heaters & Appliances: When electric current flows through a high-resistance wire, it produces heat. This principle is used in heaters, toasters, and irons. The wire gets hot and warms the surroundings.
2. Light Bulbs: An incandescent bulb has a filament with high resistance. When current passes through it, the filament heats up and glows. This produces light to brighten a room.

3. Electric Fuses: A fuse contains a thin wire with suitable resistance. If too much current flows, the wire heats up and melts. This breaks the circuit and protects appliances.

4. Resistors in Circuits: Small resistors control the flow of current in electronic circuits. They help divide voltage and protect other parts. Without resistors, devices could overheat or get damaged.

5. Speed Control: Variable resistors like rheostats change resistance as needed. They control fan speed, motor speed, or light brightness. They are also used in volume controls for audio devices.

Classification of objects on the basics of resistance :

Substance can be classified into three types based on resistance.

1. Conductor
2. insulator
3. semiconductor

Conductor:

A conductor is a material that easily allows electric current to flow because it has many free electrons. Metals like copper and aluminum are good conductors and are used in wires and circuits. They have low resistance and carry electricity efficiently.

The substance that allows the flow of electric current is easily known as a conductor, for example, Copper, iron, and gold.

Insulator:

An insulator is a material that does not allow electric current to flow through it easily because it has very few free electrons. Materials like rubber, plastic, wood, and glass are good insulators. They are used to cover wires and parts of electrical devices to prevent electric shocks and keep us safe.

Semiconductor: