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 off 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 an 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 Circuits

There are five types of electric circuits:

• Series Circuit
• Parallel Circuit
• Open Circuit
• Closed Circuit 
• leakage Circuit

Series circuit

In a series circuit, all components are connected in a single line or loop, one after another. The same electric current passes through each part, like bulbs or switches. If one bulb breaks or is removed, the whole circuit stops working because the path is cut. Series circuits are simple but not good for things that need to work alone.

Properties of the Series circuit:

• In a series circuit, there is only one path for electric current to flow.
• The same amount of current flows through all the components connected in the circuit.
• The total voltage of the power source is divided among all the components.
• If one component (like a bulb) stops working or is removed, the whole circuit stops working.
• Series circuits are simple to design and easy to connect.
• Adding more components increases the total resistance in the circuit, which reduces the current.

                     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.

Properties of the parallel  circuit:

• In a parallel circuit, there are two or more separate paths for electric current to flow.
• The total current is divided among the different branches.
• Each branch gets the same voltage as the main power source.
• If one component stops working or is removed, the other branches still work properly.
• Parallel circuits are used in homes so that lights, fans, and other devices can work independently.
• Adding more branches does not increase the total resistance, but can increase the total current used.

Open circuit 

An open circuit is a circuit where the path for electric current is broken or incomplete, so electricity cannot flow. This means any device connected to it will not work because the current cannot reach it.

Features of an Open Circuit:

• The electric path is broken or has a gap.
• No current flows through the circuit.
• Devices like bulbs or fans will not work in an open circuit.
• A switch in the “off” position makes a circuit open.

Closed circuit:

• A closed circuit is an electric circuit in which electric current can flow. A closed circuit is a circuit where the path has not been interrupted or “opened” at some point so that the current will flow.
• A closed circuit is a circuit where the path for electric current is complete and unbroken, so electricity can flow easily. This allows connected devices to work properly because the current can reach them.

Leakage circuit: 

A leakage circuit is a faulty or unsafe circuit where some electric current escapes from the normal path and flows through an unwanted path. This can happen because of damaged wires, poor insulation, or moisture. Leakage current can be dangerous and may cause electric shocks or fire.

Features of a Leakage Circuit:

• Some current leaks out of the main circuit path.
• It is caused by damaged wires, broken insulation, or wet conditions.
• Leakage current wastes electricity and can be unsafe.
• Good insulation and safety devices help prevent leakage.

Mixed circuit:

 A mixed circuit is a combination of both series and parallel circuits in the same electrical system. Some parts of the circuit are connected in series, while others are connected in parallel. This type of circuit is common in many electronic devices because it combines the advantages of both types.

Features of a Mixed Circuit:

• Contains both series and parallel connections.
• Current and voltage behave differently in different parts of the circuit.
• If one part in a series section breaks, only that section is affected, but parallel parts can still work.
• Used in complex electrical systems to improve performance and ensure safety.

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 parallel combinations

Resistors are in a 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 a parallel  combination

Two or more resistances are said to be connected in parallel if their components are connected across a 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 reciprocals 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.

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

I_{eqv =}  I₁ + I₂ …………………………….(1)

Applying Ohm’s law to the individual resistor as

Ohm’s Law 

Ohm’s Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them. Mathematically, it is written as:

V=I×R

Where:

• V is the voltage (in volts, V)
• I is the current (in amperes, A)
• R is the resistance (in ohms, Ω)

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

Kirchhoff’s Current Law 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 the 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 KCL 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.