Question

The effective resistance in series combination of two equal resistance is ‘s’. When they are joined parallel the total resistance is ‘p’. if s=np then the minimum possible value of ‘n’ is
(1) 4
(2) 1
(3) 2
(4) 3

Answer 1

Hint: The net resistance in a series connection is the sum of resistances used Whereas, the net resistance in a parallel connection, the reciprocal of equivalent resistance is the sum of reciprocals of the individual resistances. Thus by substituting the values of s and p in the given equation will the value of n.

Complete step by step answer:
Let the resistance of a single resistor be R.
The effective resistance in series combination of two equal resistance is ‘s’.
Here ‘s’ is equal to the sum of two resistors ‘R’.
That is,
s=R+R
s=2R …………….(1)
The effective resistance in parallel combination of two equal resistance is ‘p’.
Here, the reciprocal of equivalent resistance is the sum of reciprocals of individual resistances ‘R’.
That is,
$\dfrac{1}{p}=\dfrac{1}{R}+\dfrac{1}{R}$
$\dfrac{1}{p}=\dfrac{2}{R}$………….(2)
Given that,
$s=np$
$\Rightarrow \dfrac{s}{p}=n$ …………….(3)
Then substituting equation (1) and (2) in equation (3) we get,
$n=2R\times \dfrac{2}{R}$
$n=4$

So, the correct answer is “Option 1”.

Note: The net resistance in a series connection is the sum of resistances connected in the given circuit. Whereas, the net resistance in a parallel connection, that is the reciprocal of equivalent resistance is the sum of reciprocals of the individual resistances. Hence while calculating the equivalent resistance, first note whether it is connected in series or parallel. Then use the suitable equation of the given circuit.