Parallel Circuits
In a parallel circuit, components are connected across the same two points, creating multiple paths for current to flow. Voltage across each branch is the same.
Key Characteristics:
- Voltage (V): Same across all branches
- Current (I): Divided between branches
- Total Resistance (Rtotal): Found using reciprocal formula
1 / Rtotal = 1 / R₁ + 1 / R₂ + 1 / R₃ + ...
Example 1: Finding Total Resistance
Two resistors (6 Ω and 3 Ω) are connected in parallel. What is the total resistance?
Formula: 1 / Rtotal = 1 / R₁ + 1 / R₂
Calculation: 1 / Rtotal = 1/6 + 1/3 = 0.167 + 0.333 = 0.5
Rtotal: 1 / 0.5 = 2 Ω
Answer: The total resistance is 2 ohms.
Example 2: Finding Total Current
A 12 V supply powers two resistors in parallel: 4 Ω and 6 Ω. What is the total current?
Voltage across both: 12 V (same in parallel)
Current in 4 Ω: I = V / R = 12 / 4 = 3 A
Current in 6 Ω: 12 / 6 = 2 A
Total current: Itotal = 3 A + 2 A = 5 A
Answer: Total current drawn from the source is 5 amperes.