🔋College Physics I – Introduction Unit 20 – Electric Current, Resistance, and Ohm's Law

Key Concepts and Definitions

• Electric current ($I$) the flow of electric charge through a conductor, measured in amperes (A)
• Resistance ($R$) opposes the flow of electric current, measured in ohms ($\Omega$)
  • Conductors materials that allow electric current to flow easily (copper, silver, gold)
  • Insulators materials that resist the flow of electric current (rubber, plastic, glass)
• Voltage ($V$) the potential difference between two points in an electric circuit, measured in volts (V)
  • Voltage sources provide the energy needed to move electric charges through a circuit (batteries, power supplies)
• Ohm's law relates voltage, current, and resistance in a linear circuit: $V = IR$
• Power ($P$) the rate at which electrical energy is converted into other forms of energy (heat, light, motion), measured in watts (W)
  • Power is calculated using the formula: $P = IV$

Fundamentals of Electric Current

• Electric current is the flow of electric charge carriers (electrons) through a conductor
• Current is measured in amperes (A), where 1 A = 1 coulomb of charge passing a point per second
• Conventional current assumes positive charges flow from positive to negative terminals
  • In reality, electrons (negative charges) flow from negative to positive terminals
• Current can be direct (DC) or alternating (AC)
  • DC current flows in one direction and has a constant magnitude (batteries)
  • AC current periodically reverses direction and varies in magnitude (household outlets)
• Current density ($J$) is the amount of current flowing through a unit cross-sectional area of a conductor
  • $J = I/A$, where $A$ is the cross-sectional area of the conductor
• Drift velocity the average velocity of charge carriers in a conductor due to an applied electric field

Understanding Resistance

• Resistance is the opposition to the flow of electric current in a conductor
  • Measured in ohms ($\Omega$), where 1 $\Omega$ = 1 V/A
• Resistivity ($\rho$) is an intrinsic property of a material that determines its resistance
  • Resistivity depends on the material's composition and temperature
  • $R = \rho L/A$, where $L$ is the length of the conductor and $A$ is its cross-sectional area
• Conductance ($G$) is the reciprocal of resistance and measures a material's ability to conduct electric current
  • $G = 1/R$, measured in siemens (S)
• Factors affecting resistance:
  • Material properties (resistivity)
  • Geometry (length and cross-sectional area)
  • Temperature (resistance generally increases with temperature for metals)
• Resistors are circuit components designed to have a specific resistance value
  • Used to control current, divide voltage, and dissipate power in circuits

Ohm's Law Explained

• Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, provided the temperature remains constant
  • Mathematically: $V = IR$, where $V$ is voltage, $I$ is current, and $R$ is resistance
• Ohm's law is valid for linear circuit elements (ideal resistors) but not for nonlinear elements (diodes, transistors)
• Rearranging Ohm's law:
  • $I = V/R$ (current is directly proportional to voltage and inversely proportional to resistance)
  • $R = V/I$ (resistance is directly proportional to voltage and inversely proportional to current)
• Ohm's law can be applied to individual components or entire circuits
  • For series circuits: $V_{total} = V_1 + V_2 + ... + V_n$ and $R_{total} = R_1 + R_2 + ... + R_n$
  • For parallel circuits: $I_{total} = I_1 + I_2 + ... + I_n$ and $1/R_{total} = 1/R_1 + 1/R_2 + ... + 1/R_n$

Circuit Components and Diagrams

• Voltage sources provide the energy to move charges through a circuit (batteries, generators)
  • Ideal voltage sources maintain a constant voltage regardless of the current drawn
• Current sources provide a constant current regardless of the voltage across them
• Resistors oppose the flow of current and dissipate power as heat
  • Fixed resistors have a constant resistance value
  • Variable resistors (potentiometers, rheostats) allow for adjustable resistance
• Capacitors store electric charge and energy in an electric field between two conductors
  • Capacitance ($C$) is the ratio of the charge stored to the voltage applied: $C = Q/V$, measured in farads (F)
• Inductors store energy in a magnetic field generated by the current flowing through them
  • Inductance ($L$) relates the voltage induced to the rate of change of current: $V = L(dI/dt)$, measured in henries (H)
• Switches control the flow of current by opening or closing a circuit path
• Circuit diagrams use standardized symbols to represent components and their interconnections
  • Lines represent wires or conductors
  • Nodes are points where two or more components connect

Practical Applications and Examples

• Electrical wiring in buildings and homes
  • Proper wire gauge selection based on expected current and power requirements
  • Grounding and circuit protection (fuses, circuit breakers) for safety
• Lighting systems (incandescent, fluorescent, LED)
  • Resistors used to limit current and control brightness
  • Dimmer switches use variable resistance to adjust light intensity
• Electronic devices (smartphones, computers, televisions)
  • Complex circuits with numerous components (resistors, capacitors, inductors, transistors)
  • Voltage regulation and power management for optimal performance and efficiency
• Automotive electrical systems
  • Battery provides DC voltage to power various components
  • Alternator generates AC voltage to charge the battery and power the system while the engine is running
  • Fuses protect circuits from excessive current
• Heating elements (electric stoves, hair dryers, space heaters)
  • High-resistance elements convert electrical energy into heat
  • Temperature control using variable resistance or thermostats

Common Misconceptions and FAQs

• Misconception: Current is consumed by components in a circuit
  • Reality: Current is conserved; it is the same at every point in a series circuit
• Misconception: Voltage is used up by resistors
  • Reality: Voltage is dropped across resistors, but the total voltage in a closed loop is always zero
• FAQ: What is the difference between AC and DC?
  • DC (direct current) flows in one direction with constant polarity
  • AC (alternating current) periodically reverses direction and polarity
• FAQ: Can Ohm's law be applied to nonlinear components?
  • No, Ohm's law is only valid for linear components like ideal resistors
  • Nonlinear components (diodes, transistors) have a current-voltage relationship that is not directly proportional
• FAQ: What is the difference between resistance and resistivity?
  • Resistance depends on a material's resistivity and its geometry (length, cross-sectional area)
  • Resistivity is an intrinsic property of a material that determines its resistance

Key Formulas and Equations

• Ohm's law: $V = IR$
  • $I = V/R$
  • $R = V/I$
• Power: $P = IV$
  • $P = I^2R$
  • $P = V^2/R$
• Resistivity: $R = \rho L/A$
• Conductance: $G = 1/R$
• Current density: $J = I/A$
• Series resistance: $R_{total} = R_1 + R_2 + ... + R_n$
• Parallel resistance: $1/R_{total} = 1/R_1 + 1/R_2 + ... + 1/R_n$
• Capacitance: $C = Q/V$
• Inductance: $V = L(dI/dt)$