Question

If maximum resistance from the combination of two resistance is 18ohm and minimum resistance is 4ohm find two resistance

Answer 1

If the resistors are r¹ and r²

The maximum resistance is obtained when both the resistors are connected in series

Maximum resistance = r¹ + r² = 18

The minimum resistance is obtained when both the resistors are connected in parallel

Minimum resistance =

$\frac{1}{ \frac{1}{ {r}^{1} } + \frac{1}{ {r}^{2} } } = \frac{1}{4} \\ \\ \frac{ {r}^{1} {r}^{2} }{ {r}^{1} + {r}^{2} } = 4 \\ \\ {r}^{1} {r}^{2} = 4 \times 18 = 72$

Hence the resistors must have sum as 18 and

product as 72

Hence the resistors are of 12 and 6 ohm

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Answer 2

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