Answer:
(A) Smaller resistance will be equal to 5.175 ohm
(b) Larger resistance will be equal to 15.225 ohm
Explanation:
Let the two resistances are [tex]R_1[/tex] and [tex]R_2[/tex]
It is given that when they are connected in series their equivalent resistance is 20.4 ohm
So [tex]R_!+R_2=20.4[/tex]------eqn 1
When they are connected in parallel their equivalent resistance is 3.86 ohm
So [tex]\frac{R_!R_2}{R_1+R_2}=3.86[/tex]
From equation 1
[tex]R_1R_2=3.86\times 20.4=78.744[/tex]
[tex]R_1-R_2=\sqrt{(R_1+R_2)^2-4R_!R_2}=\sqrt{(20.4)^2-4\times 78.744}=10.05[/tex] ......eqn 2
Adding eqn 1 and eqn 2
[tex]2R_1=30.45[/tex]
[tex]R_1=15.225ohm[/tex] putting this value in eqn 1
[tex]R_2=20.4-15.225=5.175ohm[/tex]
(a) Smaller resistance will be equal to 5.175 ohm
(b) Larger resistance will be equal to 15.225 ohm