Question 387: 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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