In-Depth Notes on Series Circuits and Problem Solving Steps

Rules of a Series Circuit

  • Voltage Drops: Voltage drops around the circuit are divided in proportion to the ohmic value of each component.
  • Resistances: Resistances add directly.
    • Example: R{total} = R1 + R_2
  • Current: All current flows through all parts of the circuit.
    • Therefore, the amperage on any part of the circuit is the same as the total amperage.

Example Problem

Given:

  • $R_1 = 50$ ohms
  • $R_2 = 100$ ohms
  • Power Supply = 120V

Steps to Solve the Circuit:

  1. Calculate Total Resistance:

    • R{total} = R1 + R_2 = 50 ext{ ohms} + 100 ext{ ohms} = 150 ext{ ohms}

  2. Calculate Total Current:

    • Use Ohm's Law: I = rac{V}{R}
    • I_{total} = rac{120V}{150 ext{ ohms}} = 0.8 A

  3. Calculate Total Watts:

    • Use the power formula: P = V imes I
    • P_{total} = 120V imes 0.8A = 96W

  4. Calculate Voltage Across Each Resistor:

    • For $R_1$:
      • V1 = I{total} imes R_1 = 0.8A imes 50 ext{ ohms} = 40V
    • For $R_2$:
      • V2 = I{total} imes R_2 = 0.8A imes 100 ext{ ohms} = 80V

Summary of Results:

  • Total Resistance: R_{total} = 150 ext{ ohms}
  • Total Current: I_{total} = 0.8 A
  • Total Power: P_{total} = 96W
  • Voltage across $R1$: V1 = 40V
  • Voltage across $R2$: V2 = 80V