Lecture Notes: Electric Current and Ohm's Law

Key Concepts and Definitions

• Conventional Current:

  • Flows from the positive terminal to the negative terminal of a battery, similar to how water flows from high to low position.
  • Electron flow is the opposite, flowing from negative to positive terminal.

• Current (I):

  • Defined as the rate of charge flow (ΔQ/ΔT).
  • Electric charge (Q) is measured in coulombs (C), and time (T) in seconds.
  • The unit for current is the ampere (A), where 1 A = 1 C/s.
  • An electron's charge is -1.6 x 10^-9 C.

• Ohm's Law:

  • Describes the relationship between voltage (V), current (I), and resistance (R).
  • Formula: V = I * R.
  • Voltage and current are directly related, while resistance and current are inversely related.
  • Resistance is measured in ohms (Ω).*

Practical Analogies

• Resistance and Current Flow:
  • More resistance makes it harder for current to flow, similar to how traffic flows better on a multi-lane highway compared to a single-lane highway.
  • Increasing resistance decreases current and vice versa.

Electric Power

• Power (P):
  • The product of voltage and current: P = V * I.
  • Alternative forms: P = I^2 * R and P = V^2 / R.
  • Measured in watts (W), where 1 W = 1 joule/s.

Problem Solving Examples

Example 1: Calculating Electric Charge

• Given: Current = 3.8 A, Time = 12 minutes (converted to 720 seconds).
• Find: Electric charge (Q) = I * T = 2736 C.
• Conversion to Electrons:
  • 2736 C / 1.6 x 10^-9 C/electron = ~1.71 x 10^22 electrons.*

Example 2: Current and Power with a Resistor

• Given: 9V battery, 250 Ω resistor.
• Find: Current (I) using Ohm's Law: I = V/R = 0.036 A (or 36 mA).
• Power Dissipation:
  • Power (P) = I^2 * R = 0.324 W.
  • Power delivered by battery: P = V * I = 0.324 W.

Example 3: Resistance and Power of a Light Bulb

• Given: 12V battery, Current = 150 mA (converted to 0.15 A).
• Find: Resistance (R) using Ohm's Law: R = V/I = 80 Ω.
• Power Consumption: P = V * I = 1.8 W.
• Monthly Cost Calculation:
  • Convert power to kWh, calculate cost at 11 cents/kWh.
  • Total cost for a month: 14 cents.*

Example 4: Voltage and Resistance in a Motor

• Given: Power = 50 W, Current = 400 mA (converted to 0.4 A).
• Find: Voltage (V) = P/I = 125 V.
• Resistance (R):
  • Using Ohm's Law: R = V/I = 312.5 Ω.

Example 5: Electric Current Through a Resistor

• Given: Charge = 12.5 C, Resistance = 5 kΩ, Time = 8 minutes (480 seconds).
• Find: Current (I) = Q/T = 0.026 A or 26 mA.
• Power Consumption:
  • Power (P) = I^2 * R = 3.38 W.
  • Voltage across resistor: V = I * R = 130 V.

Conclusion

• Use Ohm’s Law and power equations to solve electrical circuit problems.
• Understand relationships between voltage, current, resistance, and power for problem-solving in circuits.