Question

when two unknown resistance are connected in series and in parallel , their equivalents resistances are 9 ohm and 2 ohm respectively . what are the unknown resistances ?

Answer 1

Answers :-

Let r1 and r2 be the unknown resistances.

We are given ,

r1 + r2 = 9 (in series ) ........(I)

and

r1r2/r1 +r2 = 2 (in parallel )

so,

r1r2/9 =2

r1r2 = 18
Also,

(r1 – r2) ^2 = ( r1 + r2)^2– 4r1 r2

= 81–4*18

= 81 – 72

= 9 = (3) ^2
so,

r1 – r2 = 3 ---------(ii)

from (I) and (ii) , we have

2 r1 = 12

r1 = 6 ohm

r2 = 3 ohm

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