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Electric Current: Definition and Expression

Electric current represents the flow of electric charges through a specific area per unit time. It is measured as the rate at which electric charges move. The formula to calculate electric current is as follows:
I = Q/t
Here, I represents the current, Q is the net charge flowing through a conductor's cross-section, and t denotes the time taken for the flow. The standard unit of electric charge is the coulomb (C), equivalent to approximately 6 × 10¹⁸ electrons. The unit of electric current is the ampere (A), defined as one coulomb of charge flowing per second (1A = 1C/1s).

Electric Potential and Potential Difference

The electric potential difference between two points in an electric circuit carrying a current is the work done to move a unit charge from one point to another. The formula to calculate potential difference is:
V = W/Q
V represents the potential difference, W is the work done, and Q denotes the charge. The volt (V) is the SI unit for electric potential difference, named after Alessandro Volta. It is defined as the potential difference between two points in a current-carrying conductor where 1 joule of work is required to move 1 coulomb of charge. The measurement of potential difference is done using a voltmeter, which is connected in parallel across the points under consideration.

Electric Currents in Conductors

In conductive materials like metals, some electrons are free to move within the material. These materials are known as conductors and develop electric currents when an electric field is applied. The behavior of electric currents in conductors can be summarized as follows:

• When no electric field is present, the number of electrons traveling in any direction equals the number traveling in the opposite direction, resulting in no net electric current.
• If an electric field is applied, it creates a force directed from positive to negative charges. Electrons move in response to this force, neutralizing the charges. As long as the electrons are in motion, an electric current exists.

Ohm's Law

Ohm's Law defines the relationship between potential difference (V), current (I), and resistance (R) in a conductor. It states that the potential difference across a conductor is directly proportional to the current flowing through it, with resistance as the constant of proportionality. The formula is given as:

V = IR

Here, V is the potential difference, I represents the current, and R denotes the resistance. The SI unit of resistance is the ohm (Ω). Resistance depends on the length and cross-sectional area of the conductor, as well as the nature of the material.

Limitations of Ohm's Law

Although Ohm's Law is widely applicable, there are certain limitations to its validity. These limitations include:

• V ceases to be proportional to I.
• The relationship between V and I depends on the sign of V.
• The relationship between V and I is not unique, meaning there can be more than one value of V for the same current I.
• These limitations are observed in materials such as GaAs (gallium arsenide).

Resistivity

The resistance of a uniform metallic conductor is directly proportional to its length (l) and inversely proportional to the cross-sectional area (A). Combining both relationships, we obtain the formula:

R = ρl/A
Here, R is the resistance, ρ (rho) represents the electrical resistivity of the conductor's material, and l and A are the length and cross-sectional area, respectively. Resistivity is a characteristic property of the material and is measured in ohm-meters (Ω m).

Resistivity of Various Materials

The resistivity of a material is influenced by temperature. Alloys generally exhibit higher resistivity than their constituent metals. Certain alloys, like Nichrome, show minimal variation in resistivity with temperature. Semiconductors, on the other hand, experience a decrease in resistivity as temperature rises. Copper, aluminum, and tungsten are commonly used materials in electrical applications due to their specific resistivity properties.

Types of Resistors

Resistors are passive electronic components used to regulate electric current in a circuit. Two major types of resistors are:

• Wire-wound resistors: These resistors consist of wires wound from alloys such as manganin, constantan, nichrome, etc. They offer stable resistance values and are primarily used in applications where temperature changes need to be controlled.
• Carbon resistors: Carbon resistors are compact, cost-effective, and widely used in electronic circuits. They have higher resistance values and are represented using a color code system.

Relation of Current and Drift Velocity

When an electric field is applied, free electrons inside a conductor experience a force that causes their paths to curve. This drift of electrons, opposite to the field, results in a net transfer of electrons and the generation of current. Drift velocity refers to the average uniform velocity acquired by free electrons inside a metal due to the applied electric field.

Electrical Energy and Power

Electric power represents the rate at which electric energy is dissipated or consumed in a circuit. It is calculated using the formulas:

• P = VI
• P = I²R
• P = V²/R

Here, P denotes power, V represents potential difference, I is the current, and R represents resistance. The SI unit of electric power is the watt (W), defined as the power consumed by a device carrying 1A of current at a potential difference of 1V (1W = 1V × 1A).

Cells in Series and Parallel

Cells are devices that generate electricity by utilizing chemical energy. When multiple cells are connected in series, their positive and negative terminals are joined alternately. This arrangement increases the voltage. On the other hand, connecting cells in parallel involves connecting all the positive terminals together and all the negative terminals together. This arrangement increases the current.

Potentiometer

A potentiometer consists of a long uniform wire, often several meters in length, connected to a standard cell. The potential drop per unit length is constant throughout the wire. Potentiometers are used to compare the electromotive force (emf) of two cells, measure internal resistance, and draw no current from the voltage source being measured.

Conductors and Insulators

Conductors are substances that allow the easy passage of electric charges, offering low resistance to current flow. Examples include copper, silver, and aluminum. Insulators, on the other hand, have extremely high resistance and prevent electric current from flowing. Rubber, glass, and plastic are common insulating materials.

Coulomb's Law

Coulomb's Law is a fundamental principle in electrostatics that describes the interaction between electric charges. It states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is:

F = k * (q1 * q2) / r²

Here, F represents the force, k is the proportionality constant, q1 and q2 denote the magnitudes of the charges, and r represents the distance between them.