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Resistances n each of r ohm, when connected in parallel combination, give an equivalent resistance of R. If these resistances are connected in series, then the new combination would have a resistance equal to
- a)n R
- b)n2R
- c)R/n2
- d)R/n
Correct answer is option 'B'. Can you explain this answer?
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Solution:
Given resistances n each of r ohm, when connected in parallel combination, give an equivalent resistance of R.
Resistance in Parallel Combination:
When resistors are connected in parallel, their equivalent resistance is given by:
1/R = 1/r + 1/r + …..+ 1/r (n resistors)
1/R = n/r
R = r/n (1)
When these resistances are connected in series, then the new combination would have a resistance equal to
Resistance in Series Combination:
When resistors are connected in series, their equivalent resistance is given by:
R = r + r + …. + r (n resistors)
R = nr (2)
From equations (1) and (2), we can say that:
R (Series) = n (Parallel) × r
R (Series) = n × (r/n)
R (Series) = r
R (Series) = n × (r/n) × r
R (Series) = n × R
Hence, the correct option is (B) n2R.
Given resistances n each of r ohm, when connected in parallel combination, give an equivalent resistance of R.
Resistance in Parallel Combination:
When resistors are connected in parallel, their equivalent resistance is given by:
1/R = 1/r + 1/r + …..+ 1/r (n resistors)
1/R = n/r
R = r/n (1)
When these resistances are connected in series, then the new combination would have a resistance equal to
Resistance in Series Combination:
When resistors are connected in series, their equivalent resistance is given by:
R = r + r + …. + r (n resistors)
R = nr (2)
From equations (1) and (2), we can say that:
R (Series) = n (Parallel) × r
R (Series) = n × (r/n)
R (Series) = r
R (Series) = n × (r/n) × r
R (Series) = n × R
Hence, the correct option is (B) n2R.
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Resistances n each of r ohm, when connected in parallel combination, give an equivalent resistance of R. If these resistances are connected in series, then the new combination would have a resistance equal toa)n Rb)n2Rc)R/n2d)R/nCorrect answer is option 'B'. Can you explain this answer?
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