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  4. When two resistance R1 and R2 connected in series and introduced into the left gap of a meter bridge and a resistance of 10 Ω is introduced into the right gap, a null point is found at 60 cm from left side. When R1 and R2 are connected in parallel and introduced into the left gap, a resistance of 3 Ω is introduced into the right-gap to get null point at 40 cm from left end. The product of R 1 R 2 is Ω2

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Q. When two resistance $R_1$ and $R_2$ connected in series and introduced into the left gap of a meter bridge and a resistance of $10 \,\Omega$ is introduced into the right gap, a null point is found at $60 cm$ from left side. When $R_1$ and $R_2$ are connected in parallel and introduced into the left gap, a resistance of $3 \Omega$ is introduced into the right-gap to get null point at $40 \,cm$ from left end. The product of $R _1 R _2$ is ___$\Omega^2$

JEE MainJEE Main 2023Current Electricity

Solution:

$\frac{ R _1+ R _2}{10}=\frac{60}{40}=\frac{3}{2} $
$\Rightarrow R _1+ R _2=15$
Now $\frac{R_1 R_2}{\left(R_1+R_2\right) \times 3}=\frac{40}{60}=\frac{2}{3} $
$\Rightarrow R_1 R_2=30$