If four identical resistors, of resistance 8 ohm, are first connected in series so as to give an effective resistance , and then connected in parallel so as to give an effective resistance , then the ratio is
If four identical resistors, of resistance 8 ohm, are first connected in series so as to give an effective resistance , and then connected in parallel so as to give an effective resistance , then the ratio is
Options
When resistors are connected in series, the effective resistance is the sum of individual resistances. So, . When resistors are connected in parallel, the reciprocal of the effective resistance is the sum of reciprocals of individual resistances. So, rac{1}{R_p} = rac{1}{8} + rac{1}{8} + rac{1}{8} + rac{1}{8} = rac{4}{8} = rac{1}{2}. Therefore, . Hence, the ratio rac{R_s}{R_p} = rac{32}{2} = 16.
Marking Scheme
- 11 mark
Hint
Use the formulas for series and parallel combinations of resistors to calculate the effective resistances.
Quick Oral Answer
The ratio of effective resistances in series and parallel combinations is 16.
Analysis & Explanation
The question requires the calculation of the ratio of effective resistances when four identical resistors are connected in series and in parallel. The correct answer is 16, which is obtained by dividing the effective resistance in series by the effective resistance in parallel.
Common Mistakes
- 1Forgetting to calculate the reciprocal of the effective resistance in parallel combination.
- 2Incorrectly calculating the effective resistance in series or parallel combination.
Interesting Facts
The effective resistance in series combination is always greater than the effective resistance in parallel combination.
The ratio of effective resistances in series and parallel combinations is a measure of how much the resistances are affected by the type of combination.
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Frequently Asked Questions
How many marks does this question carry in CBSE Class 10 Science 2023?
This question carries 1 mark in the CBSE Class 10 Science 2023 examination.
Which chapter does this question come from in Science?
This question is from the chapter "Electricity" in the CBSE Class 10 Science syllabus.
What topic does this question cover in Science?
This question covers the topic "Resistance" from CBSE Class 10 Science.
What type of question is this in the CBSE Class 10 Science 2023 paper?
This is a MCQ question from Section A in the CBSE Class 10 Science 2023 paper.