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

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Two resistors when connected in parallel give the resultant resistance of \(2\)

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; but when connected in series the effective resistance becomes \(9\)

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. Calculate the value of each resistance.

Resultant resistance of parallel combination, \(R_P\) \(=\)

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Resultant resistance of series combination, \(R_S\) \(=\)

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\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,

\(R_1\) \(=\)

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(ii) If \(R_2\) \(=\) \(6\) then,

\(R_1\) \(=\)

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Did you find an error?

18. HOTS I