Question 313: Current Electricity

Question

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The
resistance of their series combination is 1 k$$\Omega $$. How much was the resistance on the left slot before
interchanging the resistances?

Accepted Answer

$${X \over l}$$ = $${{1000 - X} \over {100 - l}}$$ . . . . . (1)
When X and Y are interchanged.
$${{1000 - X} \over {l - 10}}$$ = $${X \over {100 - l + 10}}$$
$$ \Rightarrow $$$$\,\,\,$$ $${{1000 - X} \over {l - 10}}$$ = $${X \over {110 - l}}$$ . . . . . (2)
From (1)  and  (2)  we  get,
$${l \over {100 - l}}$$ = $${{110 - l} \over {l - 10}}$$
$$ \Rightarrow $$$$\,\,\,$$ $$l$$
2
$$-$$ 10 = 11000 $$-$$ 100$$l$$ $$-$$ 110$$l$$ + $$l$$
2
$$ \Rightarrow $$$$\,\,\,$$ 200$$l$$ = 11000
$$l$$ = 55 cm
Putting this value of $$l$$, in equation (1)
$${X \over {55}}$$ = $${{1000 - X} \over {100 - 55}}$$
$$ \Rightarrow $$$$\,\,\,$$ 45X = 55000 $$-$$ 55X
$$ \Rightarrow $$$$\,\,\,$$ 100X = 55000
$$ \Rightarrow $$$$\,\,\,$$ X = 550 $$\Omega $$

Answer

910 $$\Omega $$

Answer

990 $$\Omega $$

Answer

505 $$\Omega $$

Answer

550 $$\Omega $$

Current Electricity

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k$\Omega $. How much was the resistance on the left slot before interchanging the resistances?

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