Notes on Electric Current and Ohm's Law

Introduction

• Focus on basic equations and practice problems related to electric current and Ohm's Law.

Conventional Current vs. Electron Flow

• Conventional Current: Flows from positive to negative terminal (high voltage to low voltage).
• Electron Flow: Electrons flow from negative to positive terminal; opposite of conventional current.

Definition of Current

• Current (I): Rate of charge flow.
  • Formula: I = ΔQ / Δt
  • Where:
    • ΔQ = electric charge in coulombs (C)
    • Δt = time in seconds (s)
• Unit of Current: Ampere (A); 1 A = 1 C/s.
• Charge of an electron: 1.6 × 10^(-19) C (negative).

Ohm's Law

• Relationship: V = I × R
  • V = Voltage (volts), I = Current (amps), R = Resistance (ohms).
• Effects of Changing Values:
  • Increasing voltage increases current (directly related).
  • Increasing resistance decreases current (inversely related).
  • Analogy: Wider road = easier flow; narrower road = harder flow.

Electric Power

• Power (P): Rate of energy transfer.
  • Formula: P = V × I
    • Alternative forms:
      • P = I² × R
      • P = V² / R
• Unit of Power: Watts (W); 1 W = 1 J/s.

Practice Problems

Problem 1: Charge Flow Calculation

• Given: Current = 3.8 A, Time = 12 minutes.
  • Convert time: 12 minutes = 720 seconds.
• Calculate charge (Q):
  • Q = I × t = 3.8 A × 720 s = 2736 C.
• Convert charge to number of electrons:
  • Number of electrons = Q / e = 2736 C / (1.6 × 10^(-19) C/electron) = 1.71 × 10²² electrons.

Problem 2: Current Through Resistor

• Given: Voltage = 9 V, Resistance = 250 Ω.
• Calculate current (I) using Ohm's Law:
  • I = V / R = 9 V / 250 Ω = 0.036 A = 36 mA.
• Calculate power (P):
  • P = I² × R = (0.036)² × 250 = 0.324 W = 324 mW.

Problem 3: Resistance Calculation

• Given: Voltage = 12 V, Current = 150 mA (0.15 A).
• Calculate resistance (R):
  • R = V / I = 12 V / 0.15 A = 80 Ω.
• Calculate power (P):
  • P = V × I = 12 V × 0.15 A = 1.8 W.

Problem 4: Monthly Cost of Power

• Given: Power = 1.8 W, Cost = 11 cents per kWh.
• Energy consumed in a month:
  • Energy (kWh) = Power (kW) × Time (h)
  • = (1.8 W / 1000) × (30 days × 24 hours) = 1.296 kWh.
• Cost:
  • Cost = Energy × Cost per kWh = 1.296 kWh × 0.11 = 0.14356 or approximately 14 cents.

Problem 5: Motor Voltage Calculation

• Given: Power = 50 W, Current = 400 mA (0.4 A).
• Calculate voltage (V):
  • V = P / I = 50 W / 0.4 A = 125 V.
• Calculate internal resistance (R):
  • R = V / I = 125 V / 0.4 A = 312.5 Ω.

Problem 6: Current Through a Resistor

• Given: Charge = 12.5 C, Resistance = 5 kΩ, Time = 8 minutes.
• Convert time: 8 minutes = 480 seconds.
• Calculate current (I):
  • I = Q / t = 12.5 C / 480 s = 0.026 A = 26 mA.
• Calculate power consumed by the resistor:
  • P = I² × R = (0.026)² × 5000 = 3.38 W.
• Calculate voltage:
  • V = I × R = 0.026 A × 5000 Ω = 130 V.