Resistors in Parallel

Understanding Parallel Circuits

• Definition of Parallel Circuits: Components connected on separate loops.

• Current Sharing: The total current flowing into a junction equals the current flowing out; current is conserved.

• Example: Two lamps connected in parallel still allow the other to light if one fails.

Key Features of Parallel Circuits

• Real-life Application: Lights in houses are connected in parallel, maintaining full voltage even if one bulb fails.

• Voltage Consistency: Voltage across each branch is the same and equal to the supply voltage.

• Current Calculation: The supply current equals the sum of currents in each branch.

Voltage and Current in Parallel Circuits

• Current: When resistors are in parallel, the supply current equals the sum of all branch currents.

• Voltage: Any components in parallel have the same potential difference (e.g., V1 = V2 = V3).

Calculating Resistance in Parallel Circuits

• Formula: To find total resistance of resistors in parallel:

  • For multiple resistors: 1/Rt = 1/R1 + 1/R2 + 1/R3 ...

  • For two resistors: Rt = (R1 * R2) / (R1 + R2)

Implications of Adding Components in Parallel

• Key Fact: Adding components in parallel lowers the total resistance in the circuit.

Example Calculations

• Example 1: R1 = 90, R2 = 120, R3 = 180

  • Calculation: 1/Rt = 1/90 + 1/120 + 1/180 = 36

  • Result: Total resistance, Rt = 36 ohms.

• Example 2: R1 = 450, R2 = 900, R3 = 300

  • Calculation: find the lowest common denominator of 90. Result: Rt = 150 ohms.

Kirchhoff's Current Law

• Application: Use in parallel circuits to demonstrate total current behavior at junctions.