Engineering
Current Divider Rule & Thevenin Maximum Power Transfer Theorem formulas
Split parallel branch currents using opposite resistance I_1 = I_total * (R_2 / (R_1 + R_2)) and verify Thevenin load power P_L = V_th^2 * R_L / (R_th + R_L)^2 peaking at R_L = R_th.
Two separate resistive DC examples
For a specified total current entering two parallel resistive branches, branch 1 receives I_total*R2/(R1+R2). Current is inversely related to branch resistance. The two branch currents sum to the total before display rounding.
The independent Thevenin example holds source voltage and positive source resistance fixed while varying a nonnegative resistive load. Its load power peaks at RL=Rth. This is not a general complex-impedance AC calculation, and a negative-resistance active network falls outside these assumptions.
At a nonzero matched-source voltage, half the resistor dissipation is in the load and half in the source resistance. This 50% figure refers to that ideal equivalent circuit, not the overall efficiency of a physical power supply. Maximum load power and maximum efficiency are different objectives.
| Circuit Theorem Metric | Formula | Circuit Values (I=6A, R1=10, R2=20; Vth=24V, Rth=8) | Key Insight |
|---|---|---|---|
| Branch 1 Current I_1 | B2 * (B4 / (B3 + B4)) | 6 * (20 / 30) = 4.00 A | Smaller R1 carries 2x current! |
| Matched Load Power (RL=8) | (V_th^2 * R_L) / (R_th + R_L)^2 | 4,608 / 256 = 18.00 W (Peak!) | Equals V_th^2 / (4 * R_th) |
| High-Efficiency Load (RL=24) | Same formula at R_L = 24 ohms | 13,824 / 1,024 = 13.50 W | 75% efficient, but lower watts! |
Two-Branch Parallel Current Divider I_1 = I_total * (R_2 / (R_1 + R_2))
Allow nonnegative branch resistances with at least one positive. One ideal short takes all the specified current; two ideal shorts leave the split indeterminate and are rejected. Signed total current is allowed to represent reversed reference direction.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B3<0,B4<0,B3+B4<=0),"Invalid inputs",ROUND(B2 * (B4 / (B3 + B4)), 2)))Thevenin Power Delivered to Load P_L (Watts)
Use volts and ohms for watts. Positive Rth is required; a shorted load RL=0 dissipates zero power in the ideal load while the source resistor still dissipates power. The formula does not check component ratings.
=IF(COUNT(B5:B7)<>3,"Invalid inputs",IF(OR(B6<=0,B7<0),"Invalid inputs",ROUND(((B5 ^ 2) * B7) / ((B6 + B7) ^ 2), 2)))Current in branch 2
The opposite numerator is now R1. Check conservation using unrounded results when rounding would hide a small residual.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B3<0,B4<0,B3+B4<=0),"Invalid inputs",ROUND(B2*(B3/(B3+B4)),2)))Maximum power for the fixed Thevenin source
Evaluate Vth^2/(4Rth), then set RL to Rth in the general load-power formula to verify agreement.
=IF(COUNT(B5:B6)<>2,"Invalid inputs",IF(B6<=0,"Invalid inputs",ROUND(B5^2/(4*B6),2)))Try the example
Use the original values or change them to test your understanding.