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Two resistors of resistances R₁ = (300±3) and
R₂ = (500+ 4)2 are connected in series. The
equivalent resistance of the series combination?
R₂ = (500+ 4)2 are connected in series. The
equivalent resistance of the series combination?
Most Upvoted Answer
Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connec...
Equivalent Resistance Calculation
When two resistors are connected in series, the equivalent resistance (R_eq) can be calculated using the formula:
R_eq = R₁ + R₂
In this case, we have:
- R₁ = 300 ± 3 ohms
- R₂ = 500 ± 4 ohms
Step 1: Calculate the Nominal Equivalent Resistance
- R_eq = R₁ + R₂
- R_eq = 300 + 500 = 800 ohms
Step 2: Calculate the Uncertainties
For resistors in series, the uncertainties add up:
- Uncertainty in R₁ = 3 ohms
- Uncertainty in R₂ = 4 ohms
Step 3: Total Uncertainty Calculation
- Total Uncertainty = Uncertainty in R₁ + Uncertainty in R₂
- Total Uncertainty = 3 + 4 = 7 ohms
Final Result
Thus, the equivalent resistance with its uncertainty is:
- R_eq = 800 ± 7 ohms
Conclusion
The equivalent resistance of the series combination of the two resistors is 800 ohms with an uncertainty of ± 7 ohms. This means the resistance can vary between 793 ohms and 807 ohms. Understanding these calculations is crucial, especially in fields like electronics and engineering where precise values are essential.
When two resistors are connected in series, the equivalent resistance (R_eq) can be calculated using the formula:
R_eq = R₁ + R₂
In this case, we have:
- R₁ = 300 ± 3 ohms
- R₂ = 500 ± 4 ohms
Step 1: Calculate the Nominal Equivalent Resistance
- R_eq = R₁ + R₂
- R_eq = 300 + 500 = 800 ohms
Step 2: Calculate the Uncertainties
For resistors in series, the uncertainties add up:
- Uncertainty in R₁ = 3 ohms
- Uncertainty in R₂ = 4 ohms
Step 3: Total Uncertainty Calculation
- Total Uncertainty = Uncertainty in R₁ + Uncertainty in R₂
- Total Uncertainty = 3 + 4 = 7 ohms
Final Result
Thus, the equivalent resistance with its uncertainty is:
- R_eq = 800 ± 7 ohms
Conclusion
The equivalent resistance of the series combination of the two resistors is 800 ohms with an uncertainty of ± 7 ohms. This means the resistance can vary between 793 ohms and 807 ohms. Understanding these calculations is crucial, especially in fields like electronics and engineering where precise values are essential.
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Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination?
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Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination?.
Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two resistors of resistances R₁ = (300±3) andR₂ = (500+ 4)2 are connected in series. Theequivalent resistance of the series combination?.
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