First slide

combination of resistance

Question

Two resistors are connected (i) in series (ii) in parallel. The equivalent resistance in the two cases are 9 ohm and 2 ohm respectively. Then the resistances of the component resistors are

Easy

A

2 ohm and 7 ohm
B

3 ohm and 6 ohm
C

3 ohm and 9 ohm
D

5 ohm and 4 ohm

Solution

$\begin{array}{l} R_{1} + R_{2} = 9 and \frac{R_{1} R_{2}}{R_{1} + R_{2}} = 2 \Rightarrow R_{1} R_{2} = 18 \\ R_{1} - R_{2} = \sqrt{{(R_{1} + R_{2})}^{2} - 4 R_{1} R_{2}} = \sqrt{81 - 72} = 3 \\ R_{1} = 6 Ω, R_{2} = 3 Ω \end{array}$

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