Question

when two resistors are connected in series their effective resistance is 80 ohm. when they are connected in parallel their effective resistance is 20 ohm. what are the values of two resistance?

Answer 1

let two resistance be X and Y

acc. to ques.

X+Y = 80

1/X + 1/Y = 20

--- X+Y/XY=20
---XY=4

therefore X and Y are 2ohms resistance.

Hope you get your answer.

Answer 2

Let the two resistors be X and Y

The formula for finding the effective resistance-

When two resistors are connected in series:

Eff R= X+Y

So here X+Y= 80--------eq(i)

When two resistors are connected in parallel:

Eff R = 1/X + 1/Y = 1/R

So here 1/X + 1/Y = 1/20

Solving, ( X+Y )/ XY = 1/20

or, 20( X+Y )= XY

Putting the value of X+Y here...

so, 20×80= XY

so, XY= 1600

Deriving value of X from here and putting it in eq(i) and solving it further:

Y^2 - 80Y + 1600 = 0

Solving it, we get Y= 40ohm

Putting the value of y in eq(i)------

X+40=80

X= 40 ohm

Ans: Both the resistors are 40ohm.