Current Electricity and EMF

• Current electricity involves the flow of electric charge (electrons) through a conductor.
• Electric current is the rate of flow of charge, measured in amperes (A), where 1 A = 1 Coulomb/second.
• Current is conventionally defined as the direction of positive charge flow, opposite to the direction of electron flow.

Electromotive Force (EMF)

• Electromotive force (EMF) is the voltage generated by a battery or a generator.
• EMF is the "push" that causes charge to move in a circuit.
• EMF is measured in volts (V).
• EMF is the potential difference across the terminals of a source when no current is flowing.
• In a circuit, EMF is the total energy per unit charge supplied by a source.
• EMF is not a force but energy per unit charge.

Electrical Resistance

• Electrical resistance is the opposition to the flow of electric current in a material.
• Resistance is measured in ohms (Ω).
• A higher resistance means a lower current for a given voltage.
• Resistance arises from collisions between electrons and atoms in the conductor.
• Factors affecting resistance: material, length, cross-sectional area, and temperature.
• Resistance increases with increasing temperature for most conductors due to increased atomic vibrations.
• Resistivity (ρ) is an intrinsic property of a material that quantifies how strongly it resists electric current.
• Resistance (R) of a wire is given by R = ρL/A, where L is the length and A is the cross-sectional area.

Ohm's Law

• Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it.
• Mathematically, Ohm's Law is expressed as V = IR, where V is voltage, I is current, and R is resistance.
• Ohm's Law is applicable to many materials under constant physical conditions (temperature, strain).
• Materials that obey Ohm's Law are called ohmic; those that do not are non-ohmic.
• Examples of non-ohmic devices: diodes and transistors.

Circuit Analysis

• Circuit analysis involves determining the voltages, currents, and resistances in an electrical circuit.
• Circuits can be series, parallel, or combinations of both.
• Series circuits: components are connected end-to-end, so the current is the same through each component.
• The total resistance in a series circuit is the sum of individual resistances: R_total = R1 + R2 + R3 + ...
• The voltage drops across each resistor in a series circuit add up to the total voltage supplied by the source.
• Parallel circuits: components are connected side-by-side, so the voltage is the same across each component.
• The reciprocal of the total resistance in a parallel circuit is the sum of the reciprocals of individual resistances: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ...
• The total current in a parallel circuit is the sum of the currents through each branch.

Series Circuits

• In a series circuit, the current is constant throughout the circuit.
• The total resistance (R_total) is the sum of individual resistances: R_total = R1 + R2 + R3 + ....
• Voltage across each resistor (V_i) is proportional to its resistance: V_i = I * R_i.
• The sum of voltage drops across all resistors equals the source voltage: V = V1 + V2 + V3 + ....
• If one component fails (e.g., breaks), the entire circuit is open, and current stops flowing.

Parallel Circuits

• In a parallel circuit, the voltage is the same across all components.
• The reciprocal of the total resistance is the sum of the reciprocals of individual resistances: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ....
• Total current (I) is the sum of currents through each branch: I = I1 + I2 + I3 + ....
• Current through each resistor (I_i) is inversely proportional to its resistance: I_i = V / R_i.
• If one branch is open (e.g., a component fails), current continues to flow through the other branches.

Power in Electrical Circuits

• Electrical power is the rate at which electrical energy is converted into other forms of energy.
• Power (P) is measured in watts (W).
• Power can be calculated using P = VI, P = I^2 * R, or P = V^2 / R.
• In a resistor, power is dissipated as heat.
• The total power supplied by a source is equal to the sum of the power dissipated in the circuit.

Energy in Electrical Circuits

• Electrical energy is the capacity to do work using electric charge.
• Energy (E) is measured in joules (J).
• Energy can be calculated using E = Pt, where P is power and t is time.
• Commonly used unit of energy is the kilowatt-hour (kWh), which is the energy consumed by a 1 kW device operating for 1 hour.

Kirchhoff's Laws

• Kirchhoff's Current Law (KCL): The algebraic sum of currents entering a node (junction) is zero.
• KCL is based on the conservation of charge.
• Kirchhoff's Voltage Law (KVL): The algebraic sum of the voltages around any closed loop in a circuit is zero.
• KVL is based on the conservation of energy.
• KCL is used to analyze parallel circuits.
• KVL is used to analyze series circuits.

Voltage Dividers

• A voltage divider is a series circuit used to produce a specific voltage that is a fraction of the source voltage.
• The output voltage (V_out) across a resistor (R_2) in a series circuit with total resistance (R_1 + R_2) is given by: V_out = V_in * (R_2 / (R_1 + R_2)).
• Voltage dividers are used to provide different voltage levels for various components in a circuit.

Current Dividers

• A current divider is a parallel circuit used to split the total current into different paths.
• The current (I_i) through a resistor (R_i) in a parallel circuit is given by: I_i = I_total * (R_total / R_i), where R_total is the equivalent resistance of the parallel combination and I_total is the total current entering the parallel combination.
• Current dividers are used to ensure that specific amounts of current flow through individual components.

Internal Resistance

• Real voltage sources (e.g., batteries) have internal resistance (r).
• Internal resistance causes the terminal voltage to drop when current flows through the source.
• The terminal voltage (V_terminal) is given by: V_terminal = EMF - Ir, where EMF is the electromotive force and I is the current.
• Maximum power transfer occurs when the load resistance is equal to the internal resistance of the source.

Measuring Instruments

• Ammeter: Measures current; connected in series with the circuit.
• Voltmeter: Measures voltage; connected in parallel with the circuit.
• Ohmmeter: Measures resistance; connected across a component when no power is applied.
• Multimeter: A versatile instrument that can measure voltage, current, and resistance.

Circuit Analysis Techniques

• Nodal Analysis: A method used to determine the node voltages in a circuit by applying KCL at each node.
• Mesh Analysis: A method used to determine the mesh currents in a planar circuit by applying KVL to each mesh.
• Superposition Theorem: States that the response in a linear circuit due to multiple independent sources is the sum of the responses due to each source acting alone.
• Thevenin's Theorem: Any linear circuit can be replaced by an equivalent circuit consisting of a voltage source (V_th) in series with a resistance (R_th).
• Norton's Theorem: Any linear circuit can be replaced by an equivalent circuit consisting of a current source (I_n) in parallel with a resistance (R_n).

Applications of Current Electricity

• Household wiring: Parallel circuits are used so that each appliance receives the same voltage and can operate independently.
• Electronic devices: Circuits are used to control and process signals in computers, smartphones, and other devices.
• Power transmission: Electrical energy is transmitted over long distances at high voltages to minimize losses due to resistance.
• Electric motors: Convert electrical energy into mechanical energy.
• Generators: Convert mechanical energy into electrical energy.

Common Electrical Components

• Resistors: Used to limit current and provide specific voltage drops.
• Capacitors: Used to store electrical energy and block DC current.
• Inductors: Used to store energy in a magnetic field and resist changes in current.
• Diodes: Allow current to flow in one direction only.
• Transistors: Used as switches or amplifiers in electronic circuits.