InterviewSolution
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InterviewSolution
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A circuit contains an ideal battery , three resistors, and tow ideal ammeters. The ammeters read 0.2 A and 0.3 A. After two of the resistors are switched, the readings of the ammeters did not change. Find the battery current. |
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Answer» If `R_2 = R_1, I_1 = I_2 = 0.15 A` and `I_3 = 0.05A`. As the ammeters are ideal, we can conclude that the three resistors `R_1, R_2, and R` are actually CONNECTED in parallel, the equivalent resistance being `R_(EQ) = (R_1R_2R_3)/(R_1R_2+R_1R_3 + R_2R_3)` In the figure, the electric CURRENTS on each resistors and battery are shown. The readings of the two ammeters are different and, consequently, by SIMPLE symmetry considerations, resistors `R_1 and R_3` are NECESSARILY different. In other words, if we interchange `R_1 and R_3`, the readings of the ammeters will also be interchanged. Therefore, we have two possible alternatives. `R_2= R_1` (if resistors `R_2 and R_1` switched, the readings of the ammeters do not vary) or `R_2 = R_3 (R_2` and `R_3` can be switched and the ammeters do not change.) The two solutions are : If `R_2 = R_1` we obtain `I_2 = I_3 = 0.1A` and `I_1 = 0.2A`, and the battery current is `I = 0.4A`. |
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