Question

When two resistors are connected in series, their effective resistance is 80 Ω. When they are connected in parallel, their effective resistance is 20 Ω. What are the values of the two resistances? (Answer : 40 W , 40 W). Solve the problem

Answer 1

Hope u will get this!!!!

Answer 2

Answer:

$R_1\ =\ 40\ \Omega$

$R_2\ =\ 40\ \Omega$

Explanation:

Let's assume that the resistance of two resistor is R1 and R2.

then, according to question,

$R_1\ +\ R_2\ =\ 80......(1)$

$\dfrac{1}{R_1}\ +\ \dfrac{1}{R_2}\ =\ \dfrac{1}{20}$

$=>\ \dfrac{R_1.R_2}{R_1+R_2}\ =\ 20.....(2)$

from equation (1) and (2). we can write

$\dfrac{R_1.(80-R_1)}{80}\ =\ 20$

$=>\ R_1.(80-R_1)\ =\ 20\times 80$

$=>\ R_1^2-80R_1+1600\ =\ 0$

$=>\ (R_1\ -\ 40)^2\ =\ 0$

$=>\ R_1\ =\ 40$

Puttinh the value of$R_1$ in equation (1), we will get

$R_2\ =\ 40\ \Omega$

So, the value of both resistances will be 40 ohm.