Current Electricity and Ohm's Law

• Current electricity deals with the flow of electric charge in conductors.

Ohm's Law

• Ohm's Law states that the current through a conductor between two points is directly proportional to the voltage across the two points
• The constant of proportionality is resistance.
• Mathematically, Ohm's Law is expressed as V = IR, where V is voltage, I is current, and R is resistance.
• Ohm's law is only applicable if physical conditions and temperature of the conductor remains constant.
• Conductors that obey Ohm's law are called ohmic conductors.
• Not all materials obey Ohm's Law; those that do not are called non-ohmic.
• Limitations: It is not a universal law, it is only applicable for some specific materials under certain conditions.
• Temperature dependence: Ohm's Law holds true only if the temperature remains constant, as resistance changes with temperature.
• Non-linear elements: Ohm's Law is not applicable to non-linear circuit elements like diodes, transistors, etc.

Electrical Resistance

• Electrical resistance is the opposition that a substance offers to the flow of electric current.
• It is measured in ohms (Ω).
• Resistance depends on the material's resistivity (ρ), length (L), and cross-sectional area (A): R = ρL/A.
• Resistivity is an intrinsic property of a material that quantifies how strongly it resists electric current.
• Conductance (G) is the reciprocal of resistance: G = 1/R, measured in siemens (S).
• Temperature dependence: Resistance of most metals increases with temperature and resistance of semiconductors decreases with temperature.

Kirchhoff's Laws

• Kirchhoff's laws are a pair of laws that deal with the conservation of current and energy in electrical circuits.
• Kirchhoff's Current Law (KCL): The total current entering a junction is equal to the total current leaving the junction.
• KCL is based on the principle of conservation of charge.
• Kirchhoff's Voltage Law (KVL): The sum of the voltage drops around any closed loop in a circuit is equal to the sum of the voltage sources in that loop.
• KVL is based on the principle of conservation of energy.
• Sign conventions are important when applying KVL.
• These laws are fundamental to circuit analysis.

AC vs DC Current

• Direct Current (DC): Electric current that flows in one direction only.
• Typically produced by batteries and DC generators.
• Voltage and current are constant with respect to time (ideally).
• Alternating Current (AC): Electric current that periodically reverses direction and changes its magnitude continuously with time.
• Commonly supplied by power grids.
• Voltage and current vary sinusoidally with time.
• AC is more efficient for long-distance power transmission due to transformers.

Circuit Theorems

• Superposition Theorem: In a linear circuit containing multiple independent sources, the current or voltage for any element is the algebraic sum of the currents or voltages produced by each independent source acting alone.
• Useful for simplifying circuits with multiple sources.
• Thevenin's Theorem: Any linear electrical network can be replaced by an equivalent circuit consisting of a voltage source (Vth) in series with a resistor (Rth).
• Vth is the open-circuit voltage at the terminals of interest, and Rth is the equivalent resistance at those terminals when all independent sources are turned off.
• Simplifies circuit analysis by reducing complex networks to simpler equivalents.
• Norton's Theorem: Any linear electrical network can be replaced by an equivalent circuit consisting of a current source (In) in parallel with a resistor (Rn).
• In is the short-circuit current at the terminals of interest, and Rn is the equivalent resistance at those terminals when all independent sources are turned off.
• Provides an alternative simplification method to Thevenin's theorem.