Consider a complex resistive network powered by a DC voltage source V. Resistor R1 experiences a catastrophic failure, transitioning to an open circuit. Simultaneously, resistor R2... Consider a complex resistive network powered by a DC voltage source V. Resistor R1 experiences a catastrophic failure, transitioning to an open circuit. Simultaneously, resistor R2, initially dissipating power P2, experiences a temperature-dependent resistance shift described by R2(T) = R_{2,0}(1 + αT), where α is the temperature coefficient of resistance and T is the temperature of R2. Given that the ambient temperature remains constant, which statement BEST describes the resulting change in total circuit current I and the power dissipation P3 of a third resistor R3 (assuming R3 is not directly connected to either R1 or R2)? A) I decreases; P3 increases as the voltage across R3 increases due to the influence of thermal runaway in R2. B) I increases; P3 decreases due to the complex interplay between the open circuit and the resistance shift affecting the current distribution. C) I decreases; P3 increases if R3 is in series with the parallel combination of other resistors, otherwise it potentially decreases. D) I increases; P3 is unchanged since R3 is independent of the changes in R1 and R2.
Understand the Problem
The question presents a circuit analysis problem involving a DC voltage source and a complex resistive network. Resistor R1 fails as an open circuit, while resistor R2 experiences a temperature-dependent resistance change. The goal is to determine how the total circuit current I and the power dissipation P3 of resistor R3 change, considering the interaction between the open circuit, temperature shift, and overall circuit configuration.
Answer
The best answer is C) I decreases; P3 increases if R3 is in series with the parallel combination of other resistors, otherwise it potentially decreases.
C) I decreases; P3 increases if R3 is in series with the parallel combination of other resistors, otherwise it potentially decreases.
Answer for screen readers
C) I decreases; P3 increases if R3 is in series with the parallel combination of other resistors, otherwise it potentially decreases.
More Information
When R1 fails as an open circuit, the total resistance in the circuit increases, causing the total current (I) to decrease, according to Ohm's Law. The effect on P3 depends on the circuit configuration. If R3 is in series with a parallel combination, the voltage across that entire combination might increase (even with less total current) and thus P3 could increase. However, P3 could decrease in other configurations depending on the values.
Tips
Understand how changes to circuit elements affect overall resistance and current flow.
Sources
- Resistance and Ohm's Law – Physical Science - OPEN OCO - open.ocolearnok.org
- Series DC Circuits Practice Worksheet with Answers - allaboutcircuits.com
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