Electric Current, Resistance, and Ohm’s Laws

Electric Current

Electric current is the flow of electric charge through a conductor, typically measured in amperes (A). It is a fundamental concept in the study of electric circuits and forms the basis for understanding how electrical devices operate.

• Definition: Electric current (I) is the rate at which charge flows through a surface.

• Formula: , where is the charge passing through a cross-section in time .

• Direction: By convention, current flows in the direction of positive charge movement (opposite to electron flow in metals).

• Unit: 1 ampere (A) = 1 coulomb/second (C/s).

Resistance and Resistivity

Resistance is a measure of how much a material opposes the flow of electric current. Resistivity is a material property that quantifies this opposition for a given substance.

• Resistance (R): The opposition to current flow, measured in ohms (Ω).

• Formula: , where is resistivity, is the length, and is the cross-sectional area of the conductor.

• Resistivity (\(\rho\)): An intrinsic property of a material, measured in ohm-meters (Ω·m).

• Temperature Dependence: For most conductors, resistance increases with temperature.

Ohm’s Laws

Ohm’s laws describe the relationship between voltage, current, and resistance in an electrical circuit.

• Ohm’s First Law (Ohm’s Law): The current through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant.

• Formula: , where is voltage, is current, and is resistance.

• Ohm’s Second Law: Sometimes refers to the dependence of resistance on material properties and geometry: .

Resistors in Series and Parallel

Resistors can be connected in series or parallel, affecting the total resistance in a circuit.

• Series Connection: The total resistance is the sum of individual resistances.

• Formula:

• Parallel Connection: The reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

• Formula:

Example Problem

Suppose you have two resistors, 4 Ω and 6 Ω, connected in series and parallel. Calculate the equivalent resistance in each case.

• Series:

• Parallel: , so

Summary Table: Series vs. Parallel Resistors

Additional info: The provided images are not directly relevant to the explanation of electric current, resistance, or Ohm’s laws, so no images are included.