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Standard XII

Physics

Galvanometer

An unknown re...

Question

An unknown resistance $R_{1}$ is connected in series with a resistance of $10 Ω$ . This combination is connected to one gap of a meter bridge while a resistance $R_{2}$ is connected in the other gap. The balance point is at $50 c m$ . Now when the $10 Ω$ resistance is removed, the balance point shifts to $40 c m$ . The value of $R_{1}$ is (in ohms) :

20

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10

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60

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40

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Solution

The correct option is B $20$
According to the first set of data given, balanced point is obtained at $50 c m$
Thus $\frac{R_{1} + 10}{R_{2}} = \frac{50}{50}$
$⟹ R_{1} + 10 = R_{2}$
Similarly from the second set of data,
$\frac{R_{1}}{R_{2}} = \frac{40}{60}$
$⟹ R_{2} = \frac{3}{2} R_{1}$
Solving the two equations gives,
$R_{1} = 20 Ω$

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The correct option is B 20According to the first set of data given, balanced point is obtained at 50cmThus R1+10R2=5050⟹R1+10=R2Similarly from the second set of data,R1R2=4060⟹R2=32R1Solving the two equations gives, R1=20Ω