Experimental Physics

JEE Main level, numerical answer, medium

25 of 70

Question 25 of 70

When two resistance R1{R}_{1} and R2{R}_{2} connected in series and introduced into the left gap of a meter bridge and a resistance of 10Ω10\Omega is introduced into the right gap, a null point is found at 60cm60cm from left side. When R1{R}_{1} and R2{R}_{2} are connected in parallel and introduced into the left gap, a resistance of 3Ω3\Omega is introduced into the right-gap to get null point at 40cm40cm from left end. The product of R1R2{R}_{1}{R}_{2} is ______ Ω2{\Omega }^{2}

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Answer: 30

A meter bridge consists of a wire of length 1m1m 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
R1+R210=6040⇒R1+R2=15Ω\dfrac{{R}_{1}+{R}_{2}}{10}=\dfrac{60}{40} \Rightarrow {R}_{1}+{R}_{2}=15\Omega
Then for the second case, we can write

R1R2(R1+R2)×3=4060⇒R1R2=30Ω2\dfrac{{R}_{1}{R}_{2}}{\left({R}_{1}+{R}_{2}\right)\times 3}=\dfrac{40}{60} \Rightarrow {R}_{1}{R}_{2}=30{\Omega }^{2}

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