Question

The resistance of two wires is 25 ohm when connected in series and 6ohm when joined in parallel. The resistance of each wire is​

Answer 1

let resistance of first wire be R1

let resistance of second wire be R2

Rs= 25 ohm

Rp= 6ohm

R1+R2= Rs

R1+R2=25

R1= 25-R2-------------1

Rp= R1×R2/ R1 + R2

6= (25-R2)R2/ 25-R2+ R2

6= 25R2 - R2^2/ 25

6×25= 25R2 - R2^2

150 = 25R2 -R2^2

R2^2- 25R2 + 150 = 0

R2^2 + 5R2 - 25R2 + 150=0

R2( R2+ 5)- 25( R2 - 5) =0

(R2-25) (R2+5) (R2-5)=0

R2-25=0..........or R2^2-25=0

R2= 25............or R2^2= 25

R2= + or - 5

taking R2=25

R1+R2= 25

R1 =0.

( no wire except superconductors at very low temple can have 0 resistance )

therfore rejecting R2=25

taking R2 = -5 cant be possible as resistance cant be negative

Taking R2=5

R1+R2=25

R1+5=25

R1= 20 ohm

Therfore the resistance of the two words are 5ohm and 20 ohm