Understanding Resistors: Series and Parallel Circuits

Introduction to Resistors

• Objective: Determine total resistance and calculate current/potential difference in circuits with resistors.

Calculating Current with Basic Resistor

• Formula: ( R = \frac{V}{I} )
  • Where:
  • ( R ) = Resistance in ohms (Ω)
  • ( V ) = Potential difference in volts (V)
  • ( I ) = Current in amperes (A)
• Example:
  • Given a 100-ohm resistor with 5 volts:
  • To find current, rearrange formula: ( I = \frac{V}{R} = \frac{5}{100} = 0.05 ) A

Resistors in Series

• Key Fact: Total resistance in series is the sum of individual resistances.
  • Formula: ( R{total} = R1 + R2 + … + Rn )
• Example:
  • Circuit with a 100-ohm and a 50-ohm resistor:
  • Total Resistance: ( R_{total} = 100 + 50 = 150 ) Ω.
  • Current: ( I = \frac{V}{R_{total}} = \frac{20}{150} = 0.13 ) A.

Additional Problem for Practice

• Given:
  • Resistors of 20 ohms, 15 ohms, 10 ohms in series:
  • Total Resistance: ( R_{total} = 20 + 15 + 10 = 45 ) Ω.
  • Potential Difference: 10 volts.
  • Current: ( I = \frac{10}{45} = 0.22 ) A.

Calculating Potential Difference

• Given:
  • Resistors of 200 ohms and 75 ohms in series:
  • Total Resistance: ( R_{total} = 200 + 75 = 275 ) Ω.
  • Current: 0.5 A.
  • Potential Difference: ( V = I \times R_{total} = 0.5 \times 275 = 137.5 ) volts.

Resistors in Parallel

• Key Fact: Total resistance of resistors in parallel is less than the smallest individual resistor.
• Example:
  • Resistors with 150 ohms and 200 ohms in parallel:
  • ( R_{total} < 150 ) Ω (the smallest resistor).
• Reason: Two parallel paths for current lead to an increase in total current, resulting in decreased total resistance.

Conclusion

• Mastering these principles enables calculation of total resistance, current, and potential difference in circuits.
• Review workbook available for more practice problems.