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  • A resistance of 2 is connected across one gap of a meter-bridge(the length of the wire is 100cm) and an unkn

A resistance of 2 \Omega is connected across one gap of a meter-bridge(the length of the wire is 100cm) and an unknown resistance, greater than 2 \Omega is connected across the other gap. When these resistances are interchanged, the unknown resistance is

Option: 1

3 \Omega


Option: 2

2 \Omega


Option: 3

4 \Omega


Option: 4

6 \Omega


Answers (1)

best_answer

\begin{aligned} & \mathrm{R>2 \Omega} \\ & \therefore\mathrm{ 100-x>x} \\ & \text { Applying, } \mathrm{\frac{P}{Q}=\frac{R}{5}} \end{aligned}

\begin{aligned} &\text{We have}\\ & \mathrm{\frac{2}{R}=\frac{x}{100-x}\quad \quad \quad \dots(i)} \\ & \mathrm{\frac{R}{2}=\frac{x+20}{80-x}\quad \quad \quad \dots(ii)} \\ &\text{Solving Eqs. (i) and (ii), we get }\\ &\mathrm{R=3 \Omega} \end{aligned}

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Kuldeep Maurya

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