Ohm's Law and Power Notes

Ohm's Law and Power

Introduction to Ohm's Law

• Definition: Ohm’s Law expresses the relationship between Voltage (V), Current (I), and Resistance (R) in a DC circuit, discovered by German physicist Georg Ohm.
• Key Relationships:
  • The electrical current flowing through a fixed linear resistor is:
  • Directly proportional to the voltage (V) applied across it.
  • Inversely proportional to the resistance (R).
• Formula: Represents Ohm’s Law mathematically as:
  V = I imes R

Using Ohm's Law to Find Values

• By knowing any two of the three quantities (V, I, R), any other can be calculated:
  • Voltage (V):
  • Formula: V = I imes R
  • Current (I):
  • Formula: I = \frac{V}{R}
  • Resistance (R):
  • Formula: R = \frac{V}{I}

The Ohm's Law Triangle

• Visual representation to aid memory:

  • Arrange V at the top, with I and R at the bottom:

        V
       -----
      I | R
  

Transposing Ohm's Law

• Alternative forms of Ohm's law can be derived:
  • V = I imes R
  • I = \frac{V}{R}
  • R = \frac{V}{I}

Applications of Ohm's Law

• Example of a simple circuit:
  • A voltage of 1V across a 1Ω resistor results in 1A of current.
  • Ohmic vs Non-Ohmic:
  • Ohmic Devices: Resistors, cables (current is proportional to voltage).
  • Non-ohmic Devices: Transistors, diodes (do not follow Ohm's Law equivalently).

Electrical Power in Circuits

• Definition: Electrical Power (P) is the energy absorbed or produced in the circuit.
• Power indicates how effectively a device converts electrical power to other forms of energy (heat/light).
• Formula: Power is calculated using: P = V imes I
  • Unit: Watt (W)
  • Common prefixes: 1 mW = 10^{-3} W, 1 kW = 10^{3} W

Finding Power from Ohm’s Law

• Alternative forms for calculating power using Ohm’s Law:
  • P = \frac{V^2}{R}
  • P = I^2 imes R

The Power Triangle

• Visual tool for understanding power relationships:

        P
       -----
      I | V
  

Transposing the Power Equation

• Similar to Ohm's Law, we can express power in alternative forms:
  • Ex: To find current based on power and voltage or resistance:
  • I = \frac{P}{V}
  • V = \frac{P}{I}

Understanding Power Calculations

• When calculating power, if the result is:
  • Positive Power (+P): Component absorbs power.
  • Negative Power (-P): Component produces power (sources like batteries).

Power Rating of Components

• Devices have a power rating (watts) indicating maximum power conversion rate (heat/light):
  • Example: 1/4W resistor, 100W light bulb.
• Horsepower equivalence: 1 hp = 746 W.
  • Example: 2 hp motor = 1492 W.

Example Problem: Calculating Circuit Values

• Given values in a circuit:
  • Voltage: V = 24 V
  • Resistance: R = 12 \, \Omega
  • Calculations:
  1. Current: I = \frac{V}{R} = \frac{24}{12} = 2 A
  2. Power: P = V \times I = 24 \times 2 = 48 W

Power Presence in Circuits

• Power is only present when both voltage and current exist:
  • Open-circuit: Voltage present but no current (I = 0) → Power (P = 0).
  • Short-circuit: Current present but no voltage (V = 0) → Power (P = 0).
• Power forms: Heat (e.g., heaters), Mechanical Work (e.g., motors), Radiated Energy (e.g., lamps).

Final Review Questions

1. Determine the current for a circuit with an 18V battery and a lamp resistance of 3Ω:
   • I = \frac{V}{R} = \frac{18V}{3Ω} = 6 A
2. Determine the power in the same circuit:
   • P = I \times V = (6A)(18V) = 108 W
3. If voltage increases in the circuit (to 36V), find:
   • New Current: I = \frac{36V}{3Ω} = 12 A
   • New Power: P = (12A)(36V) = 432 W
   • Power example showing that doubling voltage quadruples power:
     • Ratio: \frac{432 W}{108 W} = 4

Conclusion

• Important to understand and utilize Ohm's Law effectively in electrical calculations for accurate results in circuit behavior analysis.