Question 303 of 380

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

A$910\Omega$B$990\Omega$C$505\Omega$D$550\Omega$

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Answer: (D) $550\Omega$

$\dfrac{a}{b}=\dfrac{l}{100-l}$

$a+b=1000$

$\dfrac{b}{a}=\dfrac{l-10}{110-l}$

$\dfrac{100-l}{l}=\dfrac{l-10}{110-l}$

${l}^{2}-10l=11000+{l}^{2}$

$-100 l=110 l$

$200l=11000$

$l=\dfrac{110}{2}=55$

$\dfrac{55}{45}=\dfrac{a}{b}$

$\Rightarrow a=550 \Omega b=450 \Omega$