Question

Two resistances r1 and r2 give combined resistance of 4.5 ohms when in series and 1 ohm when in parallel. the resistances will be

Answer 1

For series combination
r1+r2=4.5---------(1)
For parallel combination
r1r2/r1+r2=1
r1r2=4.5------(2) (from eq. 1 putting r1+r1=4.5)
For getting the value of r1 and r2 we have to form any another equation.
So,
(r1-r2)^2=(r1+r2)^2-4r1r2
(r1-r2)^2=(4.5)^2-4*4.5
(r1-r2)^2=20.25-18
(r1-r2)^2=2.25
r1-r2=1.5-----------(3)
Adding equation 1 and 3
r1=3 and r2=1.5

Answer 2

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