Electricity

Charge

A fundamental property of matter that cause it to experience a force in the presence of the other matter.

It comes into action when electrons are transferred from one body to other.

S.I Unit of Charge

• Coulomb ( 1 coulomb is equals to 6.25 × 10¹⁸ e^- )

Define 1 Coulomb.

The amount of charge transported by a current of one ampere in one second.

Properties of Charge

Fundamental :

Like charges repel and unlike charges attract each other.

Conservation of charge :

The net charge in an isolated system is constant.

Quantization of charge :

Charge can only exists in the form of integral multiple of charge at one electron. (Q= ± ne)

Additivity :

Charges are additive in nature.

Mathematically, if a system has multiple charges of q1, q2, q3, ...qn, then the total charge Qtotal is given by:

Qtotal = q1 + q2 + q3 + ... + qn

There are two types of charge : Positive (+) and Negative (-) . 

Electric Current

The rate of flow of charge is called electric current.

• S.I Unit is Ampere, 1 Ampere = 1coulomb per second.
• If 1 coulomb charge is passing through a cross section per second is said to be one Ampere.
• It is measured by Ammeter.

Formula to measure Electric Current flowing in a wire is I = Q/T  

Electric Potential

The amount of work done is bringing a unit positive charge from infinity to a point is called as electrical potential at that point.

• It is a scalar quantity
• S.I unit is Volt, 1V = 1 Joule per coulomb.

Formula to calculate Voltage, V =  Work Done (W)  / Amount of Charge (Q)

Electric Potential Difference ΔV

The amount of work done in bringing one unit positive charge from one point to another is referred to as electric potential difference between them.

Define 1 Volt.

If one Joule work is done to bring unit charge from one point to another, the potential difference will be one volt.

V_a - v_b = w_{b -} w_{a ∕} q

Voltmeter

The potential difference between any two points in an electric field is measured by an instrument called voltmeter. It is always connected in parallel.

Electric Circuit

A closed and continuous path through which electric current flows is known as an electric circuit.

What is Electric Circuit Diagram?

A pictorial representation of the electric devices connected in a circuit, is called a " Circuit Diagram".

Symbol of some commonly used components in circuit diagrams

An Electric Cell

A battery or a combination of cells

A plug key or a switch (Open)

A plug key or a switch (Closed)

Rheostat ( A variable resistance)

A resistor

A Voltmeter

Ammeter

A Lamp of Bulb

Ohm's Law

Given by German Physicist - George Simon Ohm

According to Ohm's Law, " At constant temperature, pressure and strain, the current flowing though a conductor is directly proportional to the potential difference across the conductor."

According to Ohm's Law, V α I ( Voltage is directly proportional to Current )

Therefore., V = R x I or I = V / I

Where., V = Voltage of Potential diff, I= Current, R= Resistance of conductor.

V - I Graph 

The graph between the potential difference (V) and the corresponding current (I) is found to be a straight line passing through the origin for Ohmic conductors. 

V - I Graph ~ Potential Diff (Y-axis), Current (X-axis) 

Resistance

It is the property of a conductor that opposes the flow of charge though it.

S.I Unit of resistance is Ohm Ω.

Define 1 Ohm.

If the potential difference across the ends of a conductor is 1 volt and the current though the conductor is 1 Ampere, the resistance of the conductor is said to be 1 Ohm.

Factors on which the Resistance of a conductor depends

The resistance R of a conductor depends on:  

• Length l - Resistance is directly proportional to length (R ∝ l)

• Area A - Resistance is inversely proportional to area (R ∝ 1/A)

                                        

Combining these proportionalities gives:

                                        

R ∝ l/A  

Adding a proportionality constant ρ (resistivity of material):

R = ρ l/A             (Resistivity formula)

Meaning:

• Doubling the length l doubles the resistance R

• Doubling the area A halves the resistance R

In short:

• Length - Resistance increases with length

• Area - Resistance decreases with area

Resistivity

Resistivity of a material can be defined as the resistance per unit length of unit cross - section of the material.

Factors on which the Resistivity of a conductor depends

• It depends on the nature of the material
• It depends on the temperature
• It is independent of the length and area of cross - section of the conductor.

R = ρ l/A             (Resistivity formula)

The resistivity formula shows that resistance of a conductor depends on:

Material & temperature

Unit of Resistivity is Ohm - metre

Series Combination of Resistors

When two or more resistors are joined end-to-end so that the same current flows through each of them, it is called a series combination of resistors.

Series Combination of Reisistors

Total Potential Difference FOR 3 RESISTORS: 

V₁ + V₂ + V₃

V = IR₁ + IR₂ + IR₃ 

IR_e = IR₁ + IR₂ + IR₃

R_equivalent = R₁ + R₂ + R₃

Parallel Combination of Resistors

When two or more resistors are connected between two common points such that the same
potential difference is applied across each of them, it is called parallel combination of resistors.

Parallel Combination of Resistors

Total current flowing in Parallel connection FOR 3 RESISTORS is, 

I = I₁ + I₂ + I₃ 

V/R = V/R₁ + V/R₂ + V/R₃

V/R = V ( R₁ + R₂ + R₃ )

R_{equivalent (parallel)} = 1/R₁ + 1/R₂ + 1/R₃

Heating Effect of Electric Current

When an electric current passes through any electric component with non-zero resistance, it produces heat that heats up the corresponding component. This phenomenon is called heating effect of electric current.

Some Important formulae used in Heating Effect of Electric Current.

H = QV

We know that, 

I = QT, or Q = IT 

Therefore, H = I x V x T or

H = VIT

We know that, I = V/R

Put the value of I in H = VIT, therefore

H = V x (V/R) x T or

H = (V²/R) x T

We know that, V = IR

Put the value of V in H = VIT, therefore

H = IR x IT

H = I²RT

[ Where., H = Heat, T = Time, Q = Charge, V = Voltage, I = Current, R = Resistance ]

What is Joule's Law of Heating?

According to Joule's law, the heat (H) produced in a conductor is directly proportional to the square of the current (I) passing through it, the resistance (R) of the conductor, and the time (t) for which the current flows. Mathematically, it can be expressed as:

H = I²RT

where:

H is the heat generated in joules (J),

I is the current in amperes (A),

R is the resistance of the conductor in ohms (Ω), and

T is the time in seconds (s).

This law essentially states that when an electric current flows through a conductor with resistance, energy is converted in the form of heat. The more current that flows or the higher the resistance of the conductor, the more heat will be generated over a given period of time.

What are the applications of Joule's Law of Heating?

Joule's law of heating has practical applications in various electrical devices and systems. For example, it is essential to consider this law when designing electrical circuits, as excessive heat generation can lead to overheating and damage to the components.

It is also the principle behind electric heaters, electric stoves, and other devices that rely on the conversion of electrical energy into heat.

Electric Power

It is defined as the rate of doing work, also the rate at which energy is consumed of produced.

Electric Power = Electric Work Done / Time Taken  [P = W / T]

It's S.I Unit is Watt named after the Scottish engineer James Watt.

If W = QV , Where Q is charge and V is Voltage

Put the value of W in [P = W / T], We get

P = QV / T

 

Since, I = Q / T 

Therefore, P = QV / T = VI 

P = VI

From Ohm's Law  I = V/R then , 

P = V²R