Question

Two resistances when connected in series give equivalent resistance 9ohm when connected in parallel give 2ohm calculate their value

Answer 1

Let the resistors be a and b respectively.

when resistors connect in series the equation evolved is -

a + b = 9 .....( 1 )

when resistors connected in parallel the equation involved is -

( a*b ) / ( a + b ) = 2

( a*b ) = 2( a + b )

.............from 1.............

( a*b ) = 18

again using 1

a*(9-a) = 18

9a - a² = 18

a² - 9a +18 =0

Now we solve the quadratic equation

or a² - 6a - 3a +18 =0

or a( a - 6 ) -3( a - 6 )

or ( a - 6 ) ( a - 3 )

-> a = 6 , 3

using first we find b

so the resistors are 3 and 6 or 6 and 3