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Question

The resistance between A and B in the given figure will be(in ohm):

20
30
90
more than 10 but less than 20

A

20

B

30

C

90

D

more than 10 but less than 20

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Solution

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The correct option is D more than 10 but less than 20
In the given circuit, suppose, $r = 10 Ω$
$r_{1} = 10 Ω$
$r_{2} = 20 Ω$
and, $r_{3} = 50 Ω$
(Please refer the diagram.)
Now, $r_{1}, r_{2}, r_{3}$ are connected in parallel. Suppose, resultant of these three resistances is $R_{e}$ .
Therefore, $\frac{1}{r_{e}} = \frac{1}{r_{1}} + \frac{1}{r_{2}} + \frac{1}{r_{3}} = \frac{1}{10} + \frac{1}{20} + \frac{1}{50} = \frac{17}{100}$
Hence, $r_{e} = \frac{100}{17} Ω$
Now, resistances $r$ and $r_{e}$ are connected in series.
Therefore, equivalent resistance in the given circuit, $R = r + r_{e}$
$R = 10 + \frac{100}{17} = \frac{270}{17} Ω$ , which is more than $10 Ω$ , but less than $20 Ω$ .

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