When these n resistances are connected in series, the resultant resistance is c) n²r.
How to determine resultant resistance?
Parallel connection: When resistors are connected in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.
Therefore, for n resistors of resistance r, the total resistance in parallel (Req₁) is:
1/Req₁ = 1/r + 1/r + ... + 1/r (n times)
Req₁ = r / n
Series connection: When resistors are connected in series, the total resistance is the sum of the individual resistances. Therefore, for n resistors of resistance r, the total resistance in series (Req₂) is:
Req₂ = r + r + ... + r (n times)
Req₂ = nr
Now, find the resultant resistance when these n resistors are connected in series given that Req₁ = r:
Substitute the expression for Req₁ from the parallel connection into the equation for Req₂:
Req₂ = nr/r
= n²r
Therefore, the resultant resistance of the n resistors when connected in series is n²r.