Current Division

Overview

Engineering reference data for Current Division in electrical engineering.

Key Formulas

Ohm's Law

$V = IR$

Voltage = Current × Resistance.

Power

$P = VI = I^2R = V^2/R$

Electrical power.

Energy

$E = Pt$

Energy = Power × Time.

Variables

Practical Example

This section demonstrates the application of the current divider formulas using a common circuit design scenario.

Problem Statement: Calculate the total resistance, total current, and individual branch currents for a current divider circuit supplied with $3.3 \text{ V}$ and containing two resistors: $R_1 = 220 \ \Omega$ and $R_2 = 47 \ \Omega$.

Step-by-Step Solution:

1. Calculate Total Parallel Resistance ($R_T$): $R_T = \frac{R_1 \cdot R_2}{R_1 + R_2} = \frac{220 \ \Omega \cdot 47 \ \Omega}{220 \ \Omega + 47 \ \Omega} = 38.7 \ \Omega$

2. Calculate Total Circuit Current ($I$): $I = \frac{U}{R_T} = \frac{3.3 \ \text{V}}{38.7 \ \Omega} = 0.085 \ \text{A} \quad (85 \ \text{mA})$

3. Calculate Current through $R_1$ ($I_1$): $I_1 = \frac{U}{R_1} = \frac{3.3 \ \text{V}}{220 \ \Omega} = 0.015 \ \text{A} \quad (15 \ \text{mA})$

4. Calculate Current through $R_2$ ($I_2$): $I_2 = \frac{U}{R_2} = \frac{3.3 \ \text{V}}{47 \ \Omega} = 0.070 \ \text{A} \quad (70 \ \text{mA})$

Key Insight: Notice that $I_1 + I_2 = 15 \ \text{mA} + 70 \ \text{mA} = 85 \ \text{mA}$, which equals the total current $I$, satisfying Kirchhoff's Current Law. The branch with the lower resistance ($R_2$) carries the majority of the total current.

References

• Original Source