HOTS I — task. Science State Board, Class 10.

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Two resistors when connected in parallel give the resultant resistance of $2$

$Ω$ ; but when connected in series the effective resistance becomes $9$

$Ω$ . Calculate the value of each resistance.

Resultant resistance of parallel combination,

$R_P$

$=$

$Ω$

Resultant resistance of series combination,

$R_S$

$=$

$Ω$

$\begin{array}{l} \frac{1}{R_{P}} = \frac{i}{i_{i}} + \frac{i}{i_{i}} \\ \frac{1}{i} = \frac{i_{i} + i_{i}}{i_{i} i_{i}} \end{array}$

$i_{i} i_{i} = i (i_{i} + i_{i})$ ---- (eq. 1)

Since,

$R_S$

$=$

$R_1 + R_2$ we get

$=$

$R_1 + R_2$

$R_1$

$=$

$-R_2$ ---- (eq. 2)

On substituting (eq. 2) in (eq. 1), we get

${i_{i}}^{i} - i i_{i} + i = 0$

On factorising the above equation, we get

$R_2$

$=$

(i) If

$R_2$

$=$

$3$ then,

$R_1$

$=$

$Ω$

(ii) If

$R_2$

$=$

$6$ then,

$R_1$

$=$

$Ω$

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18. HOTS I

Exercise condition: