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: $R<em>{total} = R</em>1 + R_2$
• 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:

   • $R<em>{total} = R</em>1 + R_2 = 50 ext{ ohms} + 100 ext{ ohms} = 150 ext{ ohms}$

2. Calculate Total Current:

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

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 $R_1$:
     • $V<em>1 = I</em>{total} imes R_1 = 0.8A imes 50 ext{ ohms} = 40V$
   • For $R_2$:
     • $V<em>2 = I</em>{total} imes R_2 = 0.8A imes 100 ext{ ohms} = 80V$

Summary of Results:

• Total Resistance: $R_{total} = 150 ext{ ohms}$
• Total Current: $I_{total} = 0.8 A$
• Total Power: $P_{total} = 96W$
• Voltage across $R1$: $V</em>1 = 40V$
• Voltage across $R2$: $V</em>2 = 80V$