What is the resistance must be connected in parallel with a 1.0ohm resistance to give
an equivalent resistance of 0.2 ohm?​

Answer:

The resistance must be:

Explanation:

Remember the formula to obtain equivalent resistance:

How we know the value of the equivalent resistance (0.2 ohms) and the value of the resistance 1 (R1= 1.0 ohm), we can replace these values in the formula 1:

And we operate:

Now, we clear the variable R2:

The value is given in Ohms because that was the unit used in the other variables. In this form, you can know that the resistance that must be used to obtain an equivalent resistance of 0.2 Ohms is 0.25 Ohms in parallel with a resistance of 1.0 Ohm.

Based on the equivalent resistance and the resistance already connected, the resistance to be connected is 0.25 ohm.

The required resistance can be found as:

Equivalent resistance = (Available resistance x Required resistance) / (Available resistance + Required resistance)

Solving gives:

0.2 = (1 x R) / (1 + R)

(1 + R) x 0.2 = 1 x R

0.2 + 0.2R = R

0.2 = R - 0.2R

0.2 = 0.8R

R = 0.2/0.8

= 0.25 ohm

In conclusion, 0.25 ohm is needed.

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