Resistance Of A System Of Resistors

Key Notes:

1. Resistance of a Resistor:

  • Resistance (R) is a property that opposes the flow of electric current through a material.
  • It is measured in ohms (Ω), and the symbol for resistance is “R.”

2. Ohm’s Law:

  • Ohm’s law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) between them.
  • Mathematically: V = I × R or R = V / I.

3. Resistors in Series:

  • When resistors are connected in series, the total resistance is the sum of individual resistances.
  • Mathematically: Total Resistance (R_total) = R₁ + R₂ + R₃ + …

4. Resistors in Parallel:

  • When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.
  • Mathematically: 1 / R_total = 1 / R₁ + 1 / R₂ + 1 / R₃ + …

5. Equivalent Resistance (for Series):

  • In a series circuit, all resistors share the same current, and the equivalent resistance (R_eq) is greater than any individual resistor.
  • R_eq = R₁ + R₂ + R₃ + …

6. Equivalent Resistance (for Parallel):

  • In a parallel circuit, all resistors have the same voltage across them, and the equivalent resistance (R_eq) is less than any individual resistor.
  • 1 / R_eq = 1 / R₁ + 1 / R₂ + 1 / R₃ + …

7. Applications:

  • Understanding the resistance of a system of resistors is crucial in designing circuits and calculating the flow of current.
  • It helps in determining the power dissipation and voltage drops in different parts of a circuit.

8. Examples:

  • Example of series circuit: Christmas lights on a string.
  • Example of parallel circuit: Household electrical outlets.

9. Factors Affecting Resistance:

  • The resistance of a material depends on its length, cross-sectional area, and the resistivity of the material.

10. Practical Use:
– Calculating the resistance in real-life circuits is essential for safety and efficiency, such as in household wiring, electronic devices, and power transmission lines.

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