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Q.

The resistance of the series combination of two resistances is S. When they are joined in

parallel the total resistance is P. If S = nP, then the minimum possible value of n is

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a

4

b

3

c

2

d

1

answer is A.

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Detailed Solution

If

S = n \times P

, then the minimum possible value of n is 4.
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 substituting the values of s and p in the given equation will be the value of

n

.
Let the resistance of a single resistor be

R

.
The effective resistance in a 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 = 2 R - - - - - - - . (1)

The effective resistance in a 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,

\frac{1}{P} = \frac{1}{R} + \frac{1}{R}

\frac{1}{P} = \frac{2}{R} - - - - (2)

Given that,

s = n \times p

\Rightarrow \frac{s}{p} = n - - - - - - (3)

Then substituting equation (1) and (2) in equation (3) we get,

n = 2 R \times \frac{2}{R}

n = 2 \times 2

n = 4

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