Electric Circuit:

An electric circuit can be defined as a path through which electric current flows.

An electric circuit can also be an open circuit in which the flow of electrons is cut because the circuit is broken. Electric current doesn’t flow in an open circuit.

A simple electric circuit contains a source, a switch, a load, and a conductor. The function of these parts is described below.

•  Cell: It is used as a source to supply electric current

•  Load: It is a resistor. It is a light bulb that glows when the circuit turns on.

• Conductors: Copper wires are used as conductors with no insulation. One end of the wire carries current from the power source to the load, and the other end is from the power source.

• Switch: It is a part of the circuit that controls the supply of current in the circuit. It is used to open or close the circuit.

Types of Electric Circuit

There are five types of electric circuits:

• Open Circuit
• Closed Circuit
• Short Circuit
• Series Circuit and
• Parallel Circuit

Series circuit

A series circuit is a connection in which numerous resistances are linked one after the other.There is a single path for the flow of current.

Properties of the Series circuit:

• The same amount of current travels through every resistance.
• The supply voltage V is equal to the total individual voltage dips across the resistances.
• 

                     Fig: Series circuit diagram

                     V = V₁ + V₂  + …..+ V_n

• The equivalent electrical resistance is equivalent to the total of the individual resistances.
• The equivalent resistance is the biggest of all the individual resistances.

              R > R₁, R > R₂,….., R > R_n

Parallel circuit :

A parallel circuit is a circuit in which an electrical current passes through two or more than two paths, which is known as a parallel circuit.

In other words parallel circuit is a circuit in which numerous resistances are connected to a common point or junction is called a parallel circuit.

           Fig: Parallel circuit diagram

Properties of the parallel  circuit:

• Every component in a parallel circuit gets the same amount of voltage.
• Because the components have the same voltage but might have different resistances, the current flowing through each component can be different. The total current in the circuit is the sum of the currents through each path.
• Adding more components in parallel doesn’t change the voltage across the other components, but it does increase the total current flowing from the power source. It can also make the total resistance of the circuit lower.

Open circuit 

• an open circuit is an electric circuit in which electrical can not flow because there is a broken path.
• An open circuit is a circuit where the path has been interrupted or “opened” at some point so that the current will not flow.

An open circuit is also called an incomplete circuit.

Close circuit:

• A close circuit is an electric circuit in which electric current can flow
• A close circuit is a circuit where the path has not been interrupted or “opened” at some point so that the current will flow.

Leakage circuit: 

An earth-leakage circuit breaker (ELCB) is a safety device used in electrical installations with high Earth impedance to prevent shock.  

Mixed circuit:

 A mixed circuit is a combinational circuit. it is a combination of both series and parallel circuits. a mixed circuit contains the properties of both series and parallel circuits.

 Fig. Mixed Circuit

Properties of Mixed Circuit

• A mixed circuit combines both series and parallel arrangements of components, such as resistors
• In the parallel port, the voltage remains the same across all branches
• In the series part, the current is the same through all components.
• In the parallel part, the current divides among the branches based on their resistances.

Combination of Resistors:

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

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

Resistors are in series combination:

Two or more resistances are said to be in 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)

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

Ohm’s Law 

Ohm’s Law explains the relationship between voltage, current, and resistance in an electrical circuit:

“The current (I) flowing through a conductor is directly proportional to the voltage (V) applied across it and inversely proportional to the resistance (R).”

The formula is:

V=I×R

Where:

• $V$ is Voltage (in volts, V)
• $I$ is Current (in amperes, A)
• $R$ is Resistance (in ohms, $\Omega$)

Problem:
If a resistor of 5 ohms (R=5 Ω) is connected to a battery that provides 10 volts ($V$), find the current flowing through the resistor.

Solution: Give that

      Resistance(R) = 5Ω)

      Voltage (V) =10V

     We know that   

     V=I×RV

      I= V/R

       =10/5​

         2A

The current flowing through the resistor is 2 amperes (A).

Kirchhoff’s Current Law

(KCL) states that the total current entering a junction (or node) in an electrical circuit is equal to the total current leaving the junction. This law is based on the principle of conservation of charge, meaning that charge cannot accumulate at a junction. Kirchhoff’s current law is also known as junction law.

Mathematical Form:

At any node

∑Iin​=∑Iout​                                        

Or equivalently:                                                         

∑I=0

where ∑I=0is the algebraic sum of currents at the node, considering currents entering the node as positive and currents leaving as negative (or vice versa).

Applying CK in the above figure.

 I₁ + I₂ = I₃ + I₄ + I₅

Or,   I₁ + I₂– I₃ – I₄ – I₅ =0

Kirchhoff’s Voltage Law (KVL)

it states that the total voltage around any closed loop in an electrical circuit is equal to zero. This law is based on the principle of energy conservation, meaning that the energy gained and lost by charges as they move through the loop balances out.