An unknown resistance R 1 is connected in series with a resistance of 10 Ω . This combination is connected to one gap of the meter bridge while a resistance R 2 is connected in the other gap. The bala

Question

An unknown resistance R 1 is connected in series with a resistance of 10 Ω . This combination is connected to one gap of the meter bridge while a resistance R 2 is connected in the other gap. The balance point is at 50 cm , Now, when the 10 Ω resistance is removed the balance point shifts to 40 cm . The value of R 1 (in ohm) is

TestHub · Accepted Answer

The balance condition of a meter bridge experiment

$\frac{R}{S} = \frac{l_{1}}{(100 - l_{1})}$

Here, $R = R_{1}, S = R_{2}$

$∴ \frac{R_{1}}{R_{2}} = \frac{l_{1}}{(100 - l_{1})}$

case-I

$\frac{R_{1} + 10}{R_{2}} = \frac{50}{50}$ ...(i)

$\Rightarrow R_{1} + 10 = R_{2}$

case-II

$\frac{R_{1}}{R_{2}} = \frac{40}{60}$

$\Rightarrow R_{2} = \frac{60}{40} R_{1}$ ...(ii)

So, Eqs. (i) and (ii) give

$R_{1} + 10 = \frac{60}{40} R_{1}$

$\Rightarrow R_{1} = 20 Ω$

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