Question

When two resistors are connected in series, their effective resistance is 80 2. When they are connected in parallel, their effective resistance is 20 Q. What are the values of the two reşistances?

Answer 1

Answer:

let the value of the two resistors be x and y.

then if they connected in series

then effective resistance will be x+y

which is given equal to 80.

so x+y =80 eq 1

now if they connected in parellel.

their effective resistance will be

xy/x+y which is given equal to 20.

so xy/x+y =20 eq 2

putting value of x+y in the following eq.

we got

xy/80=20

so xy=1600

or x=1600/y

now puttin this vqlue in eq 1

we got 1600/y +y=80

or

1600 +y×y=80y

or

y^2 -80y +1600=0.

solving this quadratic eqn we will get y=40

putting value of y in eqn1 we will get x=40.

so values of resistances will be 40 and 40.