Electrical circuits: when all switches are closed, what is R?

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SUMMARY

When both switches 1 and 2 are closed in the given electrical circuit, the total resistance is 2.5 Ohms, not 7.5 Ohms as initially calculated. The confusion arises from incorrectly identifying the configuration of the resistors. Resistors connected in parallel with a closed switch effectively short-circuit the resistor, leading to a lower total resistance. The correct approach involves recognizing that the closed switches create parallel paths for the current, altering the effective resistance of the circuit.

PREREQUISITES
  • Understanding of electrical circuit theory
  • Knowledge of series and parallel resistor configurations
  • Familiarity with Ohm's Law
  • Ability to apply the formula for total resistance in parallel circuits: 1/R(T) = 1/R1 + 1/R2 + 1/R3 + 1/R4
NEXT STEPS
  • Study the principles of series and parallel circuits in detail
  • Learn how to analyze circuits with multiple switches and resistors
  • Explore practical applications of Ohm's Law in circuit design
  • Investigate the effects of short circuits on total resistance
USEFUL FOR

Students studying electrical engineering, educators teaching circuit analysis, and hobbyists building and troubleshooting electrical circuits.

GreenTea09
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Homework Statement


Hj3g5Km.jpg

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upload_2018-4-30_15-39-37.png

When both switches 1 and 2 are closed,what is the total resistance of the set up? I couldn't figure out which resistors are connected in parallel and which resistors are actually in series in this set up when both swtiches are closed. I trace back to the original current source to see if there is any splitting of the current at each section and there is, and from there i conclude they are all connected in parallel and the attempt at my solution is to calculate the total resistance of the resistors as if they are all connected in parallel. My final results in 7.5 Ohms. According to answer sheet, the correct answer should be 2.5 Ohms. The problem lies in my parallel/series circuit identification. Can anyone please advise which resistors are connected in parallel or series?

Homework Equations


1/R(T) = 1/R1 + 1/R2 + 1/R3 + 1/R4

The Attempt at a Solution


Hj3gtIW.jpg

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upload_2018-4-30_15-40-6.png
 

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Look carefully at what S1 does to the left hand resistor, and what S2 does to the right-hand resistor.
 
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Hint: What happens in a circuit when a wire is in parallel with a resistor?
 
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