**Introduction to Electric circuit:
** An electric circuit is a path in which electrons from a voltage or current source flow. The simplest electric circuit consists of three primary components: a voltage source (such as a battery), a conductive path (like wires), and a load (such as a light bulb) that consumes the electric energy. Ohm’s law and krichhoff’s laws are two fundamentals law that quantitatively define electric circuits function.

**Types of Electric Circuits
**

**Series Circuit:**

In a series circuit the Components are connected end-to-end, so the same current flows through each component. This implies that every load in the circuit must experience every bit of the circuit’s current. If one component fails, the entire circuit is interrupted.

**Parallel Circuit:**

In parallel circuit the Components are connected across common points, creating multiple paths for the current. If one path fails, the current can still flow through other paths. Each component is individually connected in a loop that extends from one end of the cell or battery to the other in a parallel circuit. One battery and two lights make up the basic parallel circuit.

**Open circuit:**

An open circuit in which no current flows. The switch being off or a disconnected wire could stop the current from the following. Following are the characteristics of open circuit:

– Since open circuit infinite resistance, current in circuit becomes zero and hence there is no voltage drop across load.

– Whole of the applied voltage is felt across the open terminals.

**Closed circuit:
**A closed circuit is one in which current flows continuously from source to load. A sudden wire break or power outage converts a closed circuit into an open circuit.

**Short circuit:
**It occurs when the positive and negative terminals of the voltage source in a circuit into contact with each other without any load between two terminals. Short circuit result in the maximum current to flow since resistance is at its minimum value.

**Mix current:**

Mix current provides both series and parallel connections for all of the components. Also known as a series-parallel circuit.

**Resistance in series and parallel circuit
**

**Resistance in series circuit:**

In a series circuit, resistors are connected end-to-end, so there is only one path for the current to flow. The total or equivalent resistance (R

_{Total}) of resistors in series is the sum of the individual resistances.

**Formula for Total Resistance in Series:
**R

_{Total = R1 + R2 + R3 + ….. + Rn}

**Example:
**Consider three resistors with resistances (R1= 2Ω, R2= 3Ω and R3=5Ω) connected in series. The total resistance is:

**R**

_{Total= }R1= 2Ω + 3Ω + 5Ω= 10Ω

**Characteristics:
**– the equivalent resistance is equal to the sum of the individual resistance, i.e. R

_{eq=}R1+ R2+ R3+…. +R

_{n}.

– The sum current flows through each resistor.

– Voltage drop across each resistor will be different, if resistors are different.

– The total power is sum of power across each resistor.

**Voltage divider rule:
** The voltage divider rule is a fundamental principle used in electrical engineering to determine the voltage across a particular component in a series circuit. This rule states that the voltage across any resistor in a series circuit is a fraction of the total voltage applied to the circuit, based on the ratio of that resistor’s value to the total resistance of the circuit.

**Resistance in Parallel Circuits:****
**In a parallel circuit, resistors are connected across the same two points, creating multiple paths for the current. The reciprocal of the total resistance (R

_{Total}) of resistors in parallel is the sum of the reciprocals of the individual resistances.

**Formula for Total Resistance in Parallel:
**R

_{Total = 1/R1 + 1/R2 + 1/R3 + ….. + 1/Rn}

After finding the reciprocal, invert the result to get the total resistance.

**Example:
**Consider three resistors with resistances (R1= 2Ω, R2= 3Ω and R3=6Ω) connected in parallel. The total resistance is calculated as:

R

_{Total = 1/}2Ω

_{ + 1/}3Ω

_{ + 1/}6Ω

first calculate the reciprocal

_{1/}2Ω

_{= 0.5 1/}3Ω

_{= 0.333 1/}6Ω= 0.167

Sum of reciprocals= 1.

final, invert sum to the total sum of resistance:

R_{Total= 1/1 = }1Ω

**Characteristics:
–** the total current is always sum of the individual currents.

– The same potential difference gets across all the resistor in parallel.

– The equivalent resistance is smallest of all the resistances.

– The equivalent conductance is the arithmetic addition of the individual conductance.

**Current divider rule:
** The current divider rule is a principle used to determine the current flowing through each branch in a parallel circuit. This rule states that the current through a particular branch in a parallel circuit is a fraction of the total current, inversely proportional to the resistance of that branch.

**Ohm’s Law
**Ohm’s Law states that the amount of current passing through a conductor is directly proportional to the voltage across the conductor, assuming physical conditions and temperature remains constant.

**formula:**V= I*R

**Ohm’s Law applications:
**– To determine the voltage, resistance or current of an electric circuit.

– To maintain the desired voltage drop across the components.

– It also simplifies power calculation.

– It provides the concept to control the flow of current.

**Kirchhoff’s law
**Ohm’s law is used to analyse current, voltage, and resistance in simple circuit but Kirchhoff’s law can be used to calculate values in complex circuits.

**Kirchhoff’s current law**this law is also known as Kirchhoff’s first law or Kirchhoff’s junction law. According to the statement, “in a closed network of conductor, the algebraic sum of current meeting at a node is point.” Alternating, current flowing towards a junction in a closed network system is equal to current flowing away from the same junction. Current exiting a junction will have a negative sign if the current entering the junction has positive sign.

For the figure shown above, applying KCL at node, we get,

I_{1}+ I_{2}+ I_{3}= I_{4}+ I_{5}

Or, I_{1}+ I_{2}+ I_{3}-I_{4} –I_{5}=0

this can be generalised to the case with n wire all connected at a node by writing:

**Kirchhoff’s voltage law**

This law is also known as Kirchhoff’s second law or Kirchhoff’s loop law. It states that, in a closed loop, the algebraic sum of all the potential differences is zero.” Alternating, in any closed loop, the algebraic sum of all electromotive force of sources and potential drops in the load is equal to zero. While one moves from lower potential to higher potential, there is gain in potential difference in direction of movement is taken as positive and while moving from higher to lower potential, there is fall in potential so this potential difference in the direction of movement is taken as negative.

for the figure shown above, applying KVL in loop, we get,

R_{1}+R_{2}+R_{3}+R_{4}+R_{5}=V_{S}

or, R_{1}+R_{2}+R_{3}+R_{4}+R_{4}-V_{S}

KVL can be generalized to any loop containing any number of components. A more formal way of writing it is