Overview
This lesson explains the concept of current division in parallel circuits, presents the current division formula, and demonstrates its application with an example.
Current Division in Parallel Circuits
- Current division applies to parallel circuits, where voltage across all branches is the same, but current divides among them.
- The current in a branch (I₁) depends on the branch resistance and the total equivalent resistance.
- In parallel, V = I₁R₁ = I₂R₂ = I₃R₃ = I_total × R_eq.
Current Division Formula
- The current through resistor R₁: I₁ = (R_eq / R₁) × I_total, where R_eq is the total parallel resistance.
- General formula for any branch n: Iₙ = (R_eq / Rₙ) × I_total.
- Alternate form using admittance (Y = 1/R): Iₙ = (Yₙ / Y_eq) × I_total, matching the voltage division format but using admittances.
Example Calculation
- For resistors R₁ = 10 Ω, R₂ = 6 Ω, R₃ = 18 Ω, and I_total = 10 A:
- Find R_eq: R_eq = 1 / (1/10 + 1/6 + 1/18) ≈ 3.103 Ω.
- I₁ = (3.103 / 10) × 10 ≈ 3.103 A.
- I₂ = (3.103 / 6) × 10 ≈ 5.172 A.
- I₃ = (3.103 / 18) × 10 ≈ 1.724 A.
- Summing branch currents approximates the total supplied current due to rounding.
Key Points for Analysis
- The smaller the resistance in a branch, the higher the current through it.
- Approximations in R_eq may lead to minor discrepancies in total current due to rounding.
- Multiple valid approaches for calculations exist as long as they're mathematically correct.
Key Terms & Definitions
- Current Division — The process by which current splits among parallel branches based on resistance.
- Parallel Circuit — A circuit where all components share the same voltage but may have different currents.
- Equivalent Resistance (R_eq) — Combined resistance of parallel resistors, found using reciprocals.
- Admittance (Y) — The reciprocal of resistance (Y = 1/R).
Action Items / Next Steps
- Prepare for nodal and mesh analysis in the next lesson.
- Review textbook sections on current division, parallel circuits, and equivalent resistance.