When two resistances and are connected in series and introduced into the left gap of a metre bridge and a resistance of is introduced into the right gap, a null point is found at 60 cm from the left side. [2023]

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Solution

Q.
When two resistances $R_{1}$ and $R_{2}$ are connected in series and introduced into the left gap of a metre bridge and a resistance of $10 Ω$ is introduced into the right gap, a null point is found at 60 cm from the left side. When $R_{1}$ and $R_{2}$ are connected in parallel and introduced into the left gap, a resistance of $3 Ω$ is introduced into the right gap to get a null point at 40 cm from the left end. The product of $R_{1} R_{2}$ is ________ $Ω^{2}$ . [2023]

Ans.
(30)

$\frac{R_{1} + R_{2}}{10} = \frac{60}{40} = \frac{3}{2} \Rightarrow R_{1} + R_{2} = 15$

$Now \frac{R_{1} R_{2}}{(R_{1} + R_{2}) \times 3} = \frac{40}{60} = \frac{2}{3} \Rightarrow R_{1} R_{2} = 30$

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