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🔋college physics i – introduction review

R_total = R1 + R2 + R3

Written by the Fiveable Content Team • Last updated August 2025
Written by the Fiveable Content Team • Last updated August 2025

Definition

R_total, or the total resistance, is the sum of the individual resistances R1, R2, and R3 in an electrical circuit. This relationship is a fundamental concept in understanding resistors in series and parallel configurations.

R_total = R1 + R2 + R3 cheat sheet for homework

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5 Must Know Facts For Your Next Test

  1. The formula $R_{total} = R_1 + R_2 + R_3$ applies to resistors connected in series, where the total resistance is the sum of the individual resistor values.
  2. In a series circuit, the same current flows through each resistor, and the voltage drops across each resistor add up to the total voltage applied to the circuit.
  3. Resistors in parallel have the same voltage drop across them, but the current divides among the parallel paths based on the individual resistor values.
  4. The reciprocal of the total resistance in a parallel circuit is the sum of the reciprocals of the individual resistor values, $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$.
  5. Understanding the relationship between total resistance and individual resistor values is crucial for analyzing and designing electrical circuits.

Review Questions

  • Explain how the formula $R_{total} = R_1 + R_2 + R_3$ applies to resistors connected in series.
    • When resistors are connected in series, the total resistance $R_{total}$ is the sum of the individual resistor values $R_1$, $R_2$, and $R_3$. In a series circuit, the same current flows through each resistor, and the voltage drops across the resistors add up to the total voltage applied to the circuit. This relationship is described by the formula $R_{total} = R_1 + R_2 + R_3$, which is a fundamental concept in understanding the behavior of resistors in series.
  • Describe how the total resistance of resistors in parallel is calculated, and explain the relationship between the individual resistor values and the total resistance.
    • For resistors connected in parallel, the total resistance $R_{total}$ is the reciprocal of the sum of the reciprocals of the individual resistor values $R_1$, $R_2$, and $R_3$. This is expressed by the formula $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. In a parallel circuit, the current divides among the parallel paths based on the individual resistor values, and the voltage drop across each resistor is the same. Understanding this relationship between the total resistance and the individual resistor values is crucial for analyzing and designing circuits with resistors in parallel.
  • Analyze how the formulas for total resistance in series and parallel circuits, $R_{total} = R_1 + R_2 + R_3$ and $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$, respectively, can be used to solve for unknown resistor values or total resistance in a circuit.
    • The formulas for total resistance in series and parallel circuits can be rearranged and used to solve for unknown resistor values or the total resistance in a circuit. For example, in a series circuit, if the total resistance and two of the individual resistor values are known, the third resistor value can be calculated using the formula $R_{total} = R_1 + R_2 + R_3$. Similarly, in a parallel circuit, if the total resistance and two of the individual resistor values are known, the third resistor value can be determined using the formula $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. This ability to solve for unknown values is essential for analyzing and designing electrical circuits with resistors in series and parallel configurations.

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