CALCULATE THE THREE RESISTORS.

Question

Three resistors R_1, R_{2, and} R₃ are connected in series-parallel with R₁ in series with the parallel combination of R₂ and R₃. The whole combination is connected across a 140 V source. Resistors R₁, R_2, and R₃ take 230 W, 250 W, and 200W respectively. Calculate the THREE RESISTORS.

Answer 1

The total power consumed = 230+250+200 = 680 watts. The total current = 680/140=4.86 amp and is the current through the single series resistance. This resistance = P/I² = 230/4.86²= 9.74 ohms = R_series. The voltage across R_series = 9.74*4.86= 47.3 volts leaving the voltage across the parallel combination to be 140-47.3= 92.7 volts. The power consumed by one of the parallel resistances = 92.7²/R₂=250watts, thus R₂= 34.4 ohms. The oower consumed by the other parallet resistance = 92.7²/R₃=200 watts, thus R₃= 43 ohms