Czy wolisz polską wersję strony elektroda?
Nie, dziękuję Przekieruj mnie tamcurrent division formula
The current divider rule states that for any set of ideal, parallel branches the branch current is
\( I_k = I_T \; \dfrac{Gk}{\displaystyle\sum{i=1}^{n} G_i}\quad\bigl(G_i = 1/R_i\bigr) \) [1],
i.e. each branch receives a share of the total current proportional to its conductance (or inversely proportional to its resistance).
Two-branch form (DC)
• Current through \(R_1\): \( I_1 = I_T \dfrac{R_2}{R_1+R_2} \)
• Current through \(R_2\): \( I_2 = I_T \dfrac{R_1}{R_1+R_2} \) [2]
Because \(R_2\) appears in the numerator of \(I_1\), the smaller resistor indeed draws the larger current—“current prefers the path of least resistance” [3].
N-branch form (DC)
• Equivalent resistance \(R{eq}=1/!\sum{i=1}^{n}!1/R_i\).
• Branch current \( I_k = IT \dfrac{R{eq}}{R_k} \) ⇔ conductance form above.
AC extension (complex impedances)
Replace \(R\) with impedance \(Z = R + jX\) and conductance with admittance \(Y = 1/Z\).
\( I_k = I_T \dfrac{Y_k}{\sum Y_i} \) keeps both magnitude and phase [4].
Worked numeric example
Parallel network: \(R_1 = 20\;\Omega\), \(R2 = 60\;\Omega\), \(V = 30\;\text{V}\).
• \(R{eq}=15\;\Omega\) → \(I_T = 30/15 = 2\;\text{A}\).
• \(I_1 = 2 \times 60/(20+60)=1.5\;\text{A}\).
• \(I_2 = 2 \times 20/(20+60)=0.5\;\text{A}\).
Check: \(I_1+I_2 = I_T\).
• Modern PCB power-distribution networks routinely place ≤5 mΩ copper planes in parallel to share >100 A CPU currents; designers still apply the same divider rule, substituting milliohm resistances of plane segments to predict hotspot currents [5].
• In switched-mode power supplies, digital controllers now compute branch admittances in real time to balance phases within ±2 %—a direct application of the admittance form of the rule [6].
Quotation: “The current in each leg of a multiphase converter is simply the total inductor current divided by the sum of inductor admittances” — Texas Instruments Power Design Seminar, 2023 [6].
• Safety: measuring branch currents may require galvanically-isolated probes; inadvertent shorts can exceed component ratings.
• Compliance: power rails in medical devices must maintain leakage <100 µA per IEC 60601—accurate current division analysis is mandatory during design audits.
• Data privacy: none directly, but simulation files often contain proprietary IP; handle according to NDA.
• Ultra-low-ohmic (<100 µΩ) current sharing: existing PCB tools lack resolution—ongoing work uses 3-D field solvers.
• AI-assisted adaptive current balancers that adjust impedances dynamically via digital potentiometers.
• Quantum and cryogenic circuits where resistance approaches zero; conventional divider rule must be modified to include kinetic inductance.
• Current divides inversely with resistance; conductance form \(I_k = I_T G_k/\Sigma G\) is universal.
• Works for DC (resistors) and AC (impedances/admittances).
• Validation requires KCL and careful tolerance/parasitic checks.
• Widely used from laboratory exercises to ≥100 A power-delivery networks, and remains an active area of research for high-density electronics.
Sources
[1] Electronics-Tutorials, “Current Divider Rule,” 2024.
[2] All About Circuits, Vol. I, Ch. 6, “Current Divider Circuits,” 2023.
[3] A. Sedra & K. Smith, Microelectronic Circuits, 8th ed., §2.4.
[4] Wikipedia, “Current Divider,” rev. Feb 2024.
[5] Intel, “VR13 Platform Power Delivery Guidelines,” App. B, 2022.
[6] Texas Instruments, Power Design Seminar SLUP402, slide 12, 2023.