R_eq = r_1 + r_2 + ... + r_n

Definition

The equation $$r_{eq} = r_1 + r_2 + ... + r_n$$ defines the equivalent resistance in a series circuit, where the total resistance is the sum of all individual resistances connected in series. This concept illustrates how resistors behave in a circuit when they are arranged one after the other, impacting the overall current flow. Understanding this equation is crucial for analyzing series circuits and designing electrical systems effectively.

5 Must Know Facts For Your Next Test

1. In a series circuit, the total voltage supplied by the source is divided among the resistors according to their resistances.
2. If one resistor in a series circuit fails (i.e., becomes an open circuit), it breaks the entire circuit, causing all components to stop functioning.
3. The equivalent resistance is always greater than any individual resistor's resistance when they are connected in series.
4. Adding more resistors in series increases the equivalent resistance, which can reduce the overall current in the circuit based on Ohm's Law.
5. The formula for calculating equivalent resistance only applies to series circuits; for parallel circuits, a different formula is used.

Review Questions

• How does adding more resistors in a series circuit affect the total current flowing through the circuit?
  • Adding more resistors in a series circuit increases the total equivalent resistance according to the formula $$r_{eq} = r_1 + r_2 + ... + r_n$$. This increase in resistance leads to a decrease in total current flowing through the circuit, as dictated by Ohm's Law, where $$I = \frac{V}{R}$$. As the equivalent resistance grows larger, it restricts the flow of current for a given voltage supply.
• Discuss how the voltage drop across individual resistors in a series circuit relates to their resistances and the total applied voltage.
  • In a series circuit, the voltage drop across each resistor is proportional to its resistance. According to Ohm's Law, if you know the total applied voltage and the equivalent resistance, you can determine how much voltage drops across each resistor. The voltage drop for each resistor can be calculated using $$V_n = I imes r_n$$, where $$I$$ is the same for all components. The sum of all individual voltage drops equals the total applied voltage, demonstrating how voltage divides in a series configuration.
• Evaluate how understanding equivalent resistance helps in designing circuits with specific performance criteria.
  • Understanding equivalent resistance is essential for designing circuits that meet specific performance criteria, such as desired current levels and power distribution. By calculating $$r_{eq} = r_1 + r_2 + ... + r_n$$, engineers can predict how adding or removing components affects overall circuit behavior. This knowledge allows for optimization of circuit designs to ensure they function effectively within their intended applications, managing factors like heat dissipation and component ratings while adhering to safety standards.

Related terms

Series Circuit: A circuit where components are connected end-to-end, resulting in the same current flowing through each component.

Ohm's Law: A fundamental principle stating that the current through a conductor between two points is directly proportional to the voltage across the two points, expressed as $$I = \frac{V}{R}$$.

Voltage Drop: The reduction in voltage across a component in a circuit due to its resistance, impacting how voltage is distributed among components.