9.4 Ohm's Law

Ohm's law is the backbone of electrical circuit analysis, linking voltage, current, and resistance. It's crucial for understanding how electricity flows and how components interact in circuits. Knowing this law helps predict circuit behavior and troubleshoot issues.

Ohm's law calculations are essential for designing and analyzing circuits. By mastering these calculations, you can determine unknown values, analyze power consumption, and understand the differences between ohmic and nonohmic materials in various electrical applications.

Ohm's Law

Ohm's law fundamentals

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• Ohm's law describes the relationship between voltage ($V$), current ($I$), and resistance ($R$) in an electrical circuit
• Current is directly proportional to voltage and inversely proportional to resistance
• [V = IR](https://www.fiveableKeyTerm:V_=_IR) is the mathematical expression of Ohm's law
  • Voltage measured in volts (V)
  • Current measured in amperes (A)
  • Resistance measured in ohms ($\Omega$)
• Doubling the voltage across a conductor with constant resistance doubles the current flowing through it (proportional increase)
• Doubling the resistance of a conductor with constant voltage halves the current flowing through it (proportional decrease)
• The electric field within a conductor drives the movement of charge carriers, resulting in current flow

Ohm's law calculations

• Ohm's law used to calculate voltage, current, or resistance when the other two quantities are known
  • Voltage calculation: $V = IR$
  • Current calculation: $I = \frac{V}{R}$
  • Resistance calculation: $R = \frac{V}{I}$
• Identify the specific portion of the circuit being analyzed and the direction of current flow before applying Ohm's law
• Series circuits have the same current through all components, and the total voltage is the sum of the individual component voltages (voltage divider)
• Parallel circuits have the same voltage across all components, and the total current is the sum of the individual component currents (current divider)

Ohmic vs nonohmic materials

• Ohmic materials exhibit a linear current-voltage relationship with constant resistance regardless of applied voltage
  • Most metals are ohmic (copper, aluminum)
  • Current-voltage graph for ohmic materials is a straight line with a slope equal to $\frac{1}{R}$
• Nonohmic materials have a nonlinear current-voltage relationship, and their resistance changes with applied voltage
  • Semiconductors (diodes, transistors), some liquids, and gases are nonohmic
  • Current-voltage graph for nonohmic materials is not a straight line, and the slope (resistance) varies with applied voltage
• Ohm's law is only valid for ohmic materials due to the requirement of constant resistance for the linear voltage-current relationship
• The conductivity of a material influences its adherence to Ohm's law

Power and Electric Potential Difference

• Power in electrical circuits is the rate at which energy is transferred or converted
• Electric potential difference (voltage) is the work done per unit charge to move a charge between two points in an electric field
• Power can be calculated using Ohm's law: $P = VI = I^2R = \frac{V^2}{R}$