General Physics: Current and Ohm's Law

Introduction

• Presenter: Chad from Chad's Prep
• Topics Covered:
  • Electrical current
  • Ohm's Law
  • Power dissipation across resistors
  • Resistivity
  • Temperature dependence of resistance

Electrical Current

• Definition: Flow of charge, symbolized by I
• Mathematical Definition: Change in charge over time
  • I = ΔQ / Δt
• SI Unit: Ampere (A)
  • 1 A = 1 C/s
• Conventional Current: Imaginary flow of positive charges, even though actual current is the flow of electrons

Ohm's Law

• Formula: ΔV = I * R
  • ΔV: Potential difference (Volts)
  • I: Current (Amperes)
  • R: Resistance (Ohms)
• Resistance (R):
  • R = ΔV / I
  • SI Unit: Ohm (Ω)
• Current Calculation: I = ΔV / R
  • Directly proportional to ΔV
  • Inversely proportional to R
• Applications:
  • Resistors in electrical appliances (e.g., light bulbs, toasters)
  • Functions to convert electrical energy into other forms of energy (heat, light)*

Power Dissipation

• Formula: P = ΔV * I
  • SI Unit: Watt (W) or Joules per second (J/s)
• Alternate Formulas:
  • P = I^2 * R
  • P = ΔV^2 / R
• Important Note: Use ΔV across the specific resistor, not necessarily the EMF source
• Example Problem:
  • Given: I = 3.0 A, R = 2.0 Ω
  • Calculation: ΔV = I * R = 6.0 V, P = ΔV * I = 18 W

Resistivity and Resistance

• Resistivity (ρ): Characteristic of a material
• Formula: R = ρ * (L/A)
  • L: Length of the wire
  • A: Cross-sectional area
• Relationships:
  • R is directly proportional to L
  • R is inversely proportional to A
• Example Problem:
  • Given: Initial R = 8.00 Ω, new wire 3x length, double radius
  • Calculation: R_new = 3/4 * 8.00 Ω = 6.00 Ω

Temperature Dependence of Resistivity

• Formula: ρ = ρ_0 * [1 + α * (T - T_0)]
  • ρ_0: Initial resistivity
  • α: Temperature coefficient
  • T: Final temperature
• Direct Proportionality: R and ρ
• Example Problem:
  • Given: R = 8.00 Ω at 20.0°C, α = 0.00393 per °C, find R at 50.0°C
  • Calculation: R_new = 8.00 * [1 + 0.00393 * (50.0 - 20.0)] = 8.94 Ω

Superconductors

• Properties: Zero resistance at low temperatures
• Current Limitation: Not practical at ambient temperatures
• Potential Benefits: Increased efficiency in power transmission (e.g., power lines)

Conclusion

• Encouragement to support and engage with Chad's Prep resources
• Happy studying!