Electric Current & Circuits Explained, Ohm's Law, Charge, Power, Physics Problems, Basic Electricity

Tutorial: Understanding Electric Current, Ohm's Law, Charge, and Power in Circuits

1. Understanding Electric Current:

• Definition: Electric current is the flow of electric charge. Conventional current states that current flows from the positive terminal to the negative terminal.
• Equation: Current (I) is defined as ΔQ/Δt, where Q is the electric charge in coulombs and t is the time in seconds. The unit of current is the ampere (amp), where 1 ampere is equal to 1 coulomb per second.
• Electron Flow: In reality, electrons flow from the negative terminal to the positive terminal, opposite to conventional current.

2. Ohm's Law Relationship:

• Equation: Ohm's Law states that V = IR, where V is voltage, I is current, and R is resistance.
• Relationships:
  • Increasing current while keeping resistance constant increases voltage.
  • Increasing voltage increases current.
  • Increasing resistance decreases current.
  • Resistance and current are inversely related.

3. Understanding Electric Power:

• Equation: Power (P) is the product of voltage and current (P = VI), or can be expressed as P = I^2 * R or P = V^2 / R.
• Unit: Power is measured in watts (W), where 1 watt is equal to 1 joule per second.

4. Practice Problems:

Problem 1:

• Given: A current of 3.8 amps flows for 12 minutes.
• Solution:
  • Calculate electric charge: Q = I * t = 3.8 A * 720 s = 2736 C.
  • Calculate number of electrons: Number of electrons = 2736 C / (1.6 * 10^-19 C) = 1.71 * 10^22 electrons.

Problem 2:

• Given: A 9V battery is connected to a 250 ohm resistor.
• Solution:
  • Calculate current: I = V / R = 9 V / 250 Ω = 0.036 A (36 mA).
  • Calculate power dissipated by the resistor: P = I^2 * R = (0.036 A)^2 * 250 Ω = 0.324 W (324 mW).
  • Calculate power delivered by the battery: P = V * I = 9 V * 0.036 A = 0.324 W.

Problem 3:

• Given: A 12V battery powers a light bulb drawing 150 mA.
• Solution:
  • Calculate electrical resistance: R = V / I = 12 V / 0.15 A = 80 Ω.
  • Calculate power consumption: P = VI = 12 V * 0.15 A = 1.8 W.
  • Calculate cost to operate: Energy = 1.8 W * 24 h/day * 30 days = 1296 Wh = 1.296 kWh. Cost = 1.296 kWh * $0.11/kWh = $0.14.

Problem 4:

• Given: A motor uses 50 W of power and draws 400 mA.
• Solution:
  • Calculate voltage across the motor: V = P / I = 50 W / 0.4 A = 125 V.
  • Calculate internal resistance of the motor: R = V / I = 125 V / 0.4 A = 312.5 Ω.

Problem 5:

• Given: 12.5 C of charge flows through a 5 kΩ resistor in 8 minutes.
• Solution:
  • Calculate current: I = Q / t = 12.5 C / 480 s = 0.026 A (26 mA).
  • Calculate power dissipated by the resistor: P = I^2 * R = (0.026 A)^2 * 5000 Ω = 3.38 W.

By following these steps and understanding the concepts of electric current, Ohm's Law, charge, and power, you can solve various problems related to basic electricity and circuits effectively.