Medium INTEGER +4 / -1 PYQ · JEE Mains 2023

When two resistance $\mathrm{R_1}$ and $\mathrm{R_2}$ 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 $\mathrm{R_1}$ and $\mathrm{R_2}$ 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 $\mathrm{R_1}$ $\mathrm{R_2}$ is ____________$\Omega^2$

Answer (integer) 30

Solution

<p>As per given information</p> <p>${{{R_1} + {R_2}} \over {10}} = {{0.6} \over {0.4}}$ ...... (1)</p> <p>& ${{{{{R_1}{R_2}} \over {{R_1} + {R_2}}}} \over 3} = {{0.4} \over {0.6}}$ ..... (2)</p> <p>$$ \Rightarrow \left. \matrix{ {R_1} + {R_2} = 15 \hfill \cr \& \,{R_1}{R_2} = 30 \hfill \cr} \right] \Rightarrow {R_1}{R_2} = 30\,{\Omega ^2}$$</p>

About this question

Subject: Physics · Chapter: Current Electricity · Topic: Wheatstone Bridge

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