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 ?

• A. $990\,\Omega$
• B. $505 \,\Omega$
• C. $550 \,\Omega$
• D. $910 \,\Omega$

Answer 1

Answer: (C)

$\frac{R_{1}}{R_{2}}=\frac{l}{(100-l)}$
$\frac{R_{2}}{R_{1}}=\frac{(l-10)}{(110-l)}$
$(100-l)(110-l)=l(l-10)$
$11000+l^2-2\,10 \,l=l^2-10\,l$
$\Rightarrow l=55 \,cm$
$R_{1}=R_{2}\left(\frac{55}{45}\right)$
$R_{1}+R_{2}=1000\, \Omega$
$R_{1}=550 \,\Omega$