Electric Circuit

Introduction to Electric Circuit

An electric circuit is a complete path through which electric current can flow.

A simple electric circuit generally consists of:

Voltage Source – such as a cell or battery
Conducting Path – such as connecting wires
Load – such as a bulb, resistor, motor, or other electrical device

When the circuit forms a complete closed path, current can flow from the source through the load.

Two important laws used for analyzing electric circuits are:

Ohm’s Law
Kirchhoff’s Laws

Basic Components of an Electric Circuit

Voltage Source

A voltage source provides the potential difference required to move electric charges through a circuit.

Examples:

Cell
Battery
DC Power Supply

Conducting Path

Conducting wires provide a path through which electric current can flow.

Copper is commonly used for electrical wiring because of its good conductivity.

Load

A load is a component that consumes electrical energy and converts it into another form of energy.

Examples:

Bulb
Heater
Motor
Resistor

Types of Electric Circuits

The major types of electric circuits discussed in this chapter are:

Series Circuit
Parallel Circuit
Open Circuit
Closed Circuit
Short Circuit
Series-Parallel or Mixed Circuit

1. Series Circuit

In a series circuit, electrical components are connected one after another in a single path.

Therefore, the same current flows through every component.

Important Characteristics

There is only one path for current.
The same current flows through all components.
If one component fails or the circuit breaks, the entire circuit stops working.
The total voltage is divided among the components.

2. Parallel Circuit

In a parallel circuit, components are connected across the same two points.

This creates multiple paths or branches for current.

Important Characteristics

There are multiple paths for current.
The voltage across each branch is the same.
Current divides among the branches.
If one branch fails, other branches may continue to operate.

For example, two bulbs connected separately across the same battery terminals form a parallel circuit.

3. Open Circuit

An open circuit is an incomplete circuit in which current cannot flow.

An open circuit can occur because of:

An open switch
A broken wire
A disconnected component

Characteristics of Open Circuit

The circuit path is incomplete.
Current becomes zero.
The open portion offers extremely high resistance.
The applied voltage may appear across the open terminals.

4. Closed Circuit

A closed circuit is a complete circuit in which current can flow continuously from the source through the load and back to the source.

When a switch is closed, the conducting path is complete.

A closed circuit can become an open circuit if:

A wire breaks
A switch opens
A connection becomes disconnected

5. Short Circuit

A short circuit occurs when two points of different potential become connected through a very low-resistance path.

For example, directly connecting the positive and negative terminals of a battery without a proper load can produce a short circuit.

Because resistance becomes very low:

Current becomes very high.

A short circuit can:

Damage electrical components
Overheat wires
Damage batteries
Cause fire hazards

6. Series-Parallel or Mixed Circuit

A series-parallel circuit, also called a mixed circuit, contains both series and parallel connections.

Some components are connected in series, while others are connected in parallel.

These circuits are common in practical electrical and electronic systems.

Resistance in Series and Parallel Circuits

Resistors can be connected in:

Series
Parallel

The total resistance depends on the type of connection.

Resistance in Series Circuit

When resistors are connected end-to-end, they are said to be connected in series.

There is only one path for current.

Formula for Total Resistance in Series

Rₜ = R₁ + R₂ + R₃ + ... + Rₙ

Where:

Rₜ = Total or equivalent resistance
R₁, R₂, R₃ ... = Individual resistances

Example of Series Resistance

Suppose:

R₁ = 2 Ω
R₂ = 3 Ω
R₃ = 5 Ω

Then:

Rₜ = R₁ + R₂ + R₃

Rₜ = 2 + 3 + 5

Therefore:

Rₜ = 10 Ω

Characteristics of Series Circuit

Equivalent resistance is the sum of individual resistances.
The same current flows through every resistor.
Voltage divides among resistors.
Different resistance values may have different voltage drops.
Total power is the sum of the power consumed by each resistor.

Voltage Divider Rule

The Voltage Divider Rule is used to calculate the voltage across a particular resistor in a series circuit.

The voltage across each resistor depends on its resistance compared with the total circuit resistance.

Formula

For resistor R₁:

V₁ = Vₜ × R₁ / Rₜ

Similarly:

V₂ = Vₜ × R₂ / Rₜ

Where:

V₁ = Voltage across R₁
V₂ = Voltage across R₂
Vₜ = Total applied voltage
Rₜ = Total resistance

Resistance in Parallel Circuit

When resistors are connected across the same two points, they are connected in parallel.

A parallel circuit provides multiple paths for current.

Formula for Total Resistance in Parallel

The correct relationship is:

1/Rₜ = 1/R₁ + 1/R₂ + 1/R₃ + ... + 1/Rₙ

After adding the reciprocals, the result is inverted to find total resistance.

Example of Parallel Resistance

Suppose:

R₁ = 2 Ω
R₂ = 3 Ω
R₃ = 6 Ω

Then:

1/Rₜ = 1/2 + 1/3 + 1/6

Using a common denominator:

1/Rₜ = 3/6 + 2/6 + 1/6

1/Rₜ = 6/6

1/Rₜ = 1

Therefore:

Rₜ = 1 Ω

Characteristics of Parallel Circuit

Total current is the sum of branch currents.
Voltage across every parallel branch is the same.
Equivalent resistance is less than the smallest individual resistance.
Current divides among different branches.
Total conductance is the sum of individual conductances.

Current Divider Rule

The Current Divider Rule is used to determine current through individual branches of a parallel circuit.

Current divides inversely according to branch resistance.

A branch having lower resistance carries more current.

For two parallel resistors:

I₁ = Iₜ × R₂ / (R₁ + R₂)

and:

I₂ = Iₜ × R₁ / (R₁ + R₂)

Where:

Iₜ = Total current
I₁ = Current through R₁
I₂ = Current through R₂

Difference Between Series and Parallel Circuits

Series Circuit	Parallel Circuit
Has one current path.	Has multiple current paths.
Same current flows through all components.	Current divides among branches.
Voltage divides among components.	Same voltage appears across branches.
Total resistance increases as resistors are added.	Total resistance decreases as parallel branches are added.
One broken component can stop the entire circuit.	Other branches may continue if one branch fails.
`Rₜ = R₁ + R₂ + ...`	`1/Rₜ = 1/R₁ + 1/R₂ + ...`

Ohm’s Law

Ohm’s Law states that:

The current flowing through a conductor is directly proportional to the potential difference across it, provided temperature and other physical conditions remain constant.

Mathematically:

V = I × R

Where:

V = Voltage
I = Current
R = Resistance

Ohm’s Law Formulae

From:

V = IR

we can derive:

Current

I = V / R

Resistance

R = V / I

Applications of Ohm’s Law

Ohm’s Law is used:

To calculate voltage
To calculate current
To calculate resistance
To determine voltage drops
To analyze electrical circuits
To help calculate electrical power
To control current through circuit components

Kirchhoff’s Laws

Ohm’s Law is useful for analyzing simple circuits.

For more complex circuits containing several loops and junctions, Kirchhoff’s Laws are very useful.

The two Kirchhoff’s Laws are:

Kirchhoff’s Current Law
Kirchhoff’s Voltage Law

1. Kirchhoff’s Current Law (KCL)

Kirchhoff’s Current Law is also called:

Kirchhoff’s First Law
Kirchhoff’s Junction Law

It states that:

At any junction or node in an electrical circuit, the total current entering the junction is equal to the total current leaving the junction.

In other words:

Total Incoming Current = Total Outgoing Current

Example of Kirchhoff’s Current Law

Suppose:

I₁, I₂ and I₃

enter a junction, while:

I₄ and I₅

leave the junction.

Then:

I₁ + I₂ + I₃ = I₄ + I₅

Rearranging:

I₁ + I₂ + I₃ - I₄ - I₅ = 0

General Form of KCL

Kirchhoff’s Current Law can be written as:

ΣI = 0

where currents entering and leaving the node are assigned opposite signs.

Basis of Kirchhoff’s Current Law

KCL is based on the conservation of electric charge.

Charge does not disappear or accumulate indefinitely at an ideal junction.

Therefore:

Current Entering = Current Leaving

2. Kirchhoff’s Voltage Law (KVL)

Kirchhoff’s Voltage Law is also called:

Kirchhoff’s Second Law
Kirchhoff’s Loop Law

It states that:

In any closed loop of an electrical circuit, the algebraic sum of all voltages is zero.

Mathematically:

ΣV = 0

Understanding KVL

While moving around a closed loop:

Moving from lower potential to higher potential is treated as a voltage rise.
Moving from higher potential to lower potential is treated as a voltage drop.

The total voltage rises must equal the total voltage drops.

Therefore:

Total Voltage Rise = Total Voltage Drop

Example of Kirchhoff’s Voltage Law

Suppose a source voltage Vₛ supplies a loop containing several resistors.

The voltage drops are:

V₁, V₂, V₃, V₄

Then:

Vₛ = V₁ + V₂ + V₃ + V₄

or:

Vₛ - V₁ - V₂ - V₃ - V₄ = 0

Since:

V = IR

the resistor voltage drops may also be written as:

Vₛ - IR₁ - IR₂ - IR₃ - IR₄ = 0

for a simple single-current loop.

Important Correction for KVL

Resistance values alone are not added directly and equated to source voltage.

For example:

R₁ + R₂ + R₃ = Vₛ

is not dimensionally correct because resistance is measured in ohms, while voltage is measured in volts.

KVL uses voltage rises and voltage drops:

ΣV = 0

Difference Between KCL and KVL

Kirchhoff’s Current Law	Kirchhoff’s Voltage Law
Also called Junction Law.	Also called Loop Law.
Applied at a node or junction.	Applied around a closed loop.
Deals mainly with current.	Deals mainly with voltage.
Incoming current equals outgoing current.	Sum of voltage rises and drops is zero.
Based on conservation of charge.	Based on conservation of energy.
Formula: `ΣI = 0`	Formula: `ΣV = 0`

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