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.