Modern Electron Theory of Matter

Modern Electron Theory of Matter

• All matter (solid, liquid, or gas) consists of minute particles called molecules.
• A molecule comprises atoms.
• Elements are molecules of the same kind of atoms.
• Compounds are molecules composed of different kinds of atoms.
• Atoms are the fundamental building blocks of matter.
• An atom has a central nucleus surrounded by orbiting electrons.
• The nucleus is the central part of an atom and contains protons (positively charged) and neutrons (no charge).
• Extra-nucleus is the outer part of the atom and contains only electrons (negatively charged).
• The charge of an electron is 1.6 x 10^-19 Coulombs.
• Force electrons (or valence electrons) are loosely attached to the nucleus of an atom.

Conductors

• Conductors are substances with a large number of free electrons at room temperature.
• Examples include silver, copper, and gold.

Insulators

• Insulators are substances that contain very few free electrons.
• Examples include plastics, rubber, and paper.

Semiconductors

• Semiconductors are materials that are neither conductors nor insulators.
• Examples include silicon, germanium, and carbon, and are used in diodes and transistors.

Electric Current

• Electric current is the flow of free electrons.
• A copper strip has a large number of free electrons, which start moving towards the positive terminal when voltage is applied.
• Electric current is the directed flow of free electrons.
• Conventional current is in opposite direction to electron flow.
• It flows from the positive to the negative terminal externally.

Electric Potential

• Electric potential is the capacity of a charged body to do work.

Potential Difference

• Potential difference is the difference in the potentials of two charged bodies.
• Electrons flow from body B to body A in the circuit if A = +5V and B = +3V and are connected.
• Current flows in a circuit if a potential difference exists; otherwise, there is no flow.
• Potential difference is called voltage.

Electromotive Force (EMF)

• EMF is energy supplied to charge by a source (like a battery).
• EMF maintains the potential difference.
• Potential difference causes current to flow.
• Potential difference across a cell becomes a voltage rise.
• Potential difference across a resistor becomes a voltage drop.

Resistance

• Resistance is the opposition offered by a substance to electric current.
• Atoms and molecules obstruct the flow of electrons, causing resistance.
• Conductors have less resistance (e.g., silver, copper, aluminum).
• Rubber and wood offer high resistance.
• Resistance depends on:
  • Length: directly proportional.
  • Cross-sectional area: inversely proportional.
  • Nature of the material.

Conductance

• Conductance is the reciprocal of resistance.

Ohm's Law

• Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R).
• It was discovered by German scientist Georg Simon Ohm.
• Ohm's Law states that the ratio of potential difference (V) across the ends of a conductor and the current (I) flowing between them is constant, provided physical conditions do not change.
• V is directly proportional to I
• V/I = constant = R, or V = IR
• Resistance of conductor between two points is 'R'.
• As voltage is applied between A and B, current flows and V/I = resistance (R)
• If voltage doubles, current also doubles.
• Voltage is measured as volts.
• Current is measured as amperes.
• Resistance is measured in ohms.

Three Forms of Ohm's Law

• I = V/R
• V = IR
• R = V/I

Definitions

• Branch: Represents a single element (either passive or active).
• Node: A connection point between two or more branches, indicated as a dot in a circuit.
• Loop: Any closed path in a circuit.
  • An independent loop (or mesh) contains no other loop inside it.
• Linear Circuit: Parameters remain constant with changes in voltage or current.
  • Examples: resistors, capacitors.
• Non-Linear Circuit: Parameters change with voltage or current.
  • Examples: semiconductors.
• Unilateral Circuit: Current flows in only one direction.
  • Example: rectifier.
• Bilateral Circuit: Current flows in both directions.
  • Example: transmission line.
• Active Circuit: Contains one or more voltage or current sources.
  • Examples: circuits with transistors, batteries, or diodes.
• Passive Circuit: Contains no energy source.
  • Examples: circuits containing resistors, inductors, or capacitors.

Kirchhoff's Laws

Kirchhoff's Current Law (KCL)

• Based on the law of charge conservation.
• Charge cannot be created nor destroyed.
• The algebraic sum of currents at a node must equal zero.
• Σ In = 0
• N is the number of branches at the node.
• In is the nth current entering or leaving the node.
• Entering currents are taken as positive.
• Leaving currents are taken as negative.

Kirchhoff's Voltage Law (KVL)

• It is based on the law of energy conservation.
• The algebraic sum of all voltages around a closed path (or loop) is zero.
• Σ Nm = 0
• M = Number of voltages in the loop.
• Vm = mth voltage.
• Apply KVL to closed loop R1, R2 R3; V1 - iR1 - iR2 + V3 - iR3 = V1
• In that case V1 + V4 = V2 + V3+ V5
• The sum of voltage rises equals the sum of voltage drops.

Series Connection of Resistances

• Resistances are connected end-to-end.
• In series, current is same in the entire circuit
• The potential difference across the circuit is equal to sum of individual resistances, V = V1 + V2 + V3.
• V = IR
• IR = IR1 + IR2 + IR3
• Req = R1 + R2 + R3
• For voltage division, if two resistances are in series:
  • V1 = I R1
  • V1 = V R1 / (R1 + R2)

Parallel Combination of Resistances

• Resistances are connected with two ends connected.
• Applying the same voltage to all resistors, current differs for all resistors.
• Whole current = sum of branch currents.
• I = I1 + I2 + I3.
• According to Ohm's law I = V/R
• 𝟏/R = V/R1 + V/R2 + V/R3
• For two resistors, Req = R1||R2 -Req = (R1 R2) / (R1 + R2)
• In that case I2 = I R1/(R1 + R2)