When three resistors, each having resistance r, are connected in parallel, their resultant resistance is x. If these three resistances are connected in series, the total resistance will be
[amp_mcq option1=”3x” option2=”3rx” option3=”9x” option4=”3/x” correct=”option3″]
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UPSC NDA-2 – 2016
$\frac{1}{x} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} = \frac{3}{r}$
So, $x = \frac{r}{3}$, which means $r = 3x$.
When these three resistors are connected in series, the total resistance is the sum of individual resistances:
Total resistance $R_{series} = r + r + r = 3r$.
Substituting the expression for $r$ in terms of $x$ ($r=3x$):
$R_{series} = 3 \times (3x) = 9x$.