Current Divider Rule

The Current Divider Rule is used to calculate the current through a branch in a parallel circuit. It helps determine how total current splits between resistors.

Formula:

If two resistors are in parallel with a total current Itotal:

Ix = (Rother / (R₁ + R₂)) × Itotal

Example 1: Two Resistors

A 10 A current flows into two parallel resistors: R₁ = 6 Ω and R₂ = 3 Ω. What is the current through R₁?

Formula: IR1 = (R₂ / (R₁ + R₂)) × Itotal

Calculation: I = (3 / (6 + 3)) × 10 = (3 / 9) × 10 = 3.33 A

Answer: The current through R₁ is 3.33 amperes.

Example 2: Unequal Branches

A 5 A current flows into two parallel resistors: R₁ = 2 Ω and R₂ = 8 Ω. What is the current through R₂?

Formula: IR2 = (R₁ / (R₁ + R₂)) × Itotal

Calculation: I = (2 / (2 + 8)) × 5 = (2 / 10) × 5 = 1 A

Answer: The current through R₂ is 1 ampere.