Parallel Circuits
- Understand parallel circuit characteristics and branching
- Apply parallel rules: same voltage, currents add, reciprocal resistance
- Calculate equivalent resistance using parallel formulas
- Understand current dividers in parallel circuits
What is a Parallel Circuit?
In a parallel circuit, components are connected across common points, creating multiple paths for current to flow. Each branch operates independently.
Parallel Circuit Visualization
Multiple paths for current - voltage is same across all branches
Parallel Circuit Rules
Rule 1: Same Voltage
The voltage is the same across all branches in a parallel circuit.
Rule 2: Currents Add
The total current is the sum of currents through each branch.
Rule 3: Reciprocal Resistance
The reciprocal of total resistance equals sum of reciprocals.
For two resistors in parallel: R_total = (R₁ × R₂) / (R₁ + R₂)
Parallel Circuit Calculator
Circuit Parameters
Calculated Results
Current Divider Rule
In parallel circuits, current divides inversely proportional to resistance.
| Configuration | Formula | Example |
|---|---|---|
| Two Resistors | I₁ = I × R₂/(R₁+R₂) | Lower R = Higher I |
| General | I_n = I × (R_eq / R_n) | More branches = less R_eq |
Why Use Parallel Circuits?
✓ Independent Operation
Each branch works independently - one component failing doesn't affect others.
✓ Constant Voltage
All components get the same full source voltage.
✓ Easy to Add Loads
Adding components doesn't reduce voltage to existing ones.
✓ Lower Total Resistance
More branches = lower equivalent resistance.
Summary
- Parallel Circuit: Multiple paths, components across common points
- Same Voltage: V is constant across all parallel branches
- Currents Add: I_total = I₁ + I₂ + I₃ + ...
- 1/R_total = 1/R₁ + 1/R₂ + ... for parallel resistance
- Two resistors: R_eq = (R₁ × R₂)/(R₁ + R₂)