Question

26.
The equivalent resistance of n resistors each of same resistance when connected in series is R. I
the same resistance are connected in parallel, the equivalent resistance will be
(A) R/n^2
(B) R/n
(C) n^2R
(D) nR​

Answer 1

Answer:

B . R/n

Explanation:

1/r +1/r+1/r+,,,,,,, n times is n/r , it is equal to the 1/R so the equivalent resistance R = R/n

Answer 2

Given,

The equivalent resistance of n resistors each of same resistance when connected in series = R

To find,

The equivalent resistance if the same resistors are connected in a parallel type of arrangement.

Solution,

We can simply solve this numerical problem by using the following process:

Let us assume the resistance of each resistor or x ohms.

Mathematically,

If a set of resistors are arranged in a series type of arrangement, then the equivalent resistance of the arrangement is equal to the total of the individual resistances. Similarly, if a set of resistors are arranged in a parallel type of arrangement, then the reciprocal of the equivalent resistance of the arrangement is equal to the sum of the reciprocals of the individual resistances.

{Statement-1}

Now, according to the question;

The equivalent resistance of n resistors each of same resistance when connected in series = R

=> x ohms × n = R ohms

{according to the statement-1}

=> x = R/n ohms

{Equation-1}

Now, according to the statement-1;

1/(equivalent resistance if the same resistors are connected in the parallel type of arrangement)

= 1/x + 1/x + -------(up to n times)

= n/x = n × 1/x = n × n/R = n^2/R

(according to equation-1)

=> the equivalent resistance if the same resistors are connected in the parallel type of arrangement = R/n^2 ohms

Hence, the equivalent resistance if the same resistors are connected in the parallel type of arrangement is equal to R/n^2 ohms. (Option-A)