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 Ω is introduced into the right gap, a null point is found at 60 cm from le

Question

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 Ω 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 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 ______ Ω 2

TestHub · Accepted Answer

A meter bridge consists of a wire of length $1 m$ and of uniform cross-sectional area stretched taut and clamped between two thick metallic strips bent at right angles with two gaps across which resistors are to be connected. It works on the principle of the Wheatstone bridge. Therefore, we can write

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

Then for the second case, we can write

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

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