Question

you are given an identical wires each of resistance R when these are connected in parallel the equivalent resistance is X when these will be connected in series the equivalent resistance will be​

Answer 1

Answer:

the equivalent resistance will be y

Answer 2

Equivalent resistance when the wires are connected in series is $n^{2}X$.

• Given, n identical wires with resistance R.
• In parallel connection, reciprocal of equivalent resistance is equal to the sum of the reciprocals of individual resistances.

                     $\frac{1}{R_{eq}}=\frac{1}{R} +\frac{1}{R}+\frac{1}{R}------ n wires$

                     $\frac{1}{R_{eq}}=\frac{n}{R}$

                     ${R_{eq}}=\frac{R}{n}$

• But equivalent resistance in parallel connection = X [given]

                      $X=\frac{R}{n}$

                  ⇒ R = nX -----------------(1)

• In series connection, equivalent resistance is equal to the sum of individual resistances.

                        $R_{ser} =R+R+R............nwires$

                        $R_{ser} =nR$

                        $R_{ser} =n(nX)$              [from (1)]

                        $R_{ser} =n^{2}X$