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Is it true that in order to get the resultant of three $9 Ω$ resistors equal to $6 Ω$ we should connect two resistors in series and one in parallel to them?

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True

False

answer is A.

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Detailed Solution

The above statement is true.
Question Image

The

9 Ω

resistor is in series with the another

9 Ω

resistors, therefore the equivalent resistance is equal to

R_{S} = 9 + 9

\Rightarrow R_{S} = 18 Ω

Now, the

9 Ω

resistor is connected in a parallel combination with another

9 Ω

resistor, we get the equivalent resistance

R

\frac{1}{R} = \frac{1}{9} + \frac{1}{R_{S}}

\Rightarrow \frac{1}{R} = \frac{1}{9} + \frac{1}{18}

\Rightarrow \frac{1}{R} = \frac{3}{18}

\Rightarrow R_{P} = 6 Ω

Hence, the equivalent resistance is equal to

6 Ω

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