The total resistance of two series-connected conductors is 10 ohms, and the parallel-connected same

The total resistance of two series-connected conductors is 10 ohms, and the parallel-connected same conductors are 2.1 ohms. Determine the value of these resistances.

Let the resistance value of the first conductor be equal to X Ohm, and the second conductor Y Ohm.

Then, when connecting the conductors in series:

X + Y = 10 ohms. (one)

And with parallel connection of conductors:

X * Y / (X + Y) = 2.1 ohms.

X * Y / 10 = 2.1 Ohm.

X * Y = 21. (2)

Let’s solve the system of equations 1 and 2.

Y = 10 – X.

X * (10 – X) = 21.

X2 – 10 * X + 21 = 0.

Let’s solve the quadratic equation.

X1 = 7 Ohm, X2 = 3 Ohm.

U1 = 3 ohms, U2 = 7 ohms.

Answer: The resistance of the conductors is 3 ohms and 7 ohms.