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