A balanced 400 V line-voltage three-phase supply feeds the shown unbalanced star: 300 Ω from each line to a floating star point, with an extra 100 Ω across the R-phase 300 Ω resistor. Find RMS voltage across the 100 Ω resistor in V.
The R branch equivalent is $300\parallel100=75$ Ω and the other branches are 300 Ω each. Let the balanced phase voltages sum to zero. Floating-neutral voltage is $V_N=(V_R/75+V_Y/300+V_B/300)/(1/75+2/300)=V_R/2$. Therefore the R-branch voltage is $V_R-V_N=V_R/2$. Its RMS magnitude is $400/(2\sqrt3)=115.47$ V, also the voltage across 100 Ω.
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