R = v/i

Definition

The equation $$r = \frac{v}{i}$$ defines resistance, where 'r' represents resistance in ohms (Ω), 'v' is the voltage across a conductor in volts (V), and 'i' is the current flowing through it in amperes (A). This relationship illustrates how resistance impedes the flow of electric current, helping to understand how electrical devices function and how they can be optimized. The formula forms a cornerstone of Ohm's Law, which describes the behavior of electrical circuits and is fundamental to analyzing electronic devices.

5 Must Know Facts For Your Next Test

1. Resistance is measured in ohms (Ω) and quantifies how much a material opposes the flow of electric current.
2. Increasing resistance in a circuit results in less current flowing for a given voltage, illustrating the inverse relationship between voltage and current when resistance is constant.
3. Materials with high resistance are often insulators, while those with low resistance are conductors.
4. Ohm's Law can be rearranged to find current and voltage as well, which makes it versatile for circuit analysis.
5. Temperature can affect resistance; as temperature increases, most conductors exhibit higher resistance due to increased atomic vibrations.

Review Questions

• How does the equation $$r = \frac{v}{i}$$ relate to circuit behavior when adjusting voltage or current?
  • The equation $$r = \frac{v}{i}$$ shows that if you increase voltage while keeping resistance constant, current will increase proportionally. Conversely, if you reduce current while maintaining voltage, resistance must increase. This relationship is crucial for understanding how adjustments to voltage or current impact overall circuit behavior and performance.
• Discuss the significance of resistance in determining whether a material is classified as a conductor or an insulator.
  • Resistance plays a key role in classifying materials. Conductors have low resistance, allowing electric currents to flow easily, while insulators possess high resistance, preventing significant current flow. Understanding this distinction helps engineers select appropriate materials for different electrical applications, ensuring efficiency and safety.
• Evaluate the impact of temperature on the resistance in electrical circuits and how this affects overall circuit performance.
  • Temperature significantly impacts resistance; as it rises, most materials exhibit increased atomic vibrations, leading to higher resistance. This change affects circuit performance by potentially reducing current flow if voltage remains constant. In practical applications, this means that devices must be designed to manage heat dissipation effectively to maintain functionality and efficiency.

Related terms

Ohm's Law: A principle that states the current through a conductor between two points is directly proportional to the voltage across the two points, expressed as $$v = i \cdot r$$.

Conductance: The reciprocal of resistance, indicating how easily electricity flows through a conductor, calculated as $$G = \frac{1}{r}$$.

Voltage: The electric potential difference between two points in a circuit, driving the flow of current.