Question

Two resistances X and Y are in the left and right gaps of a meter bridge. The balance point is 40 cm from left.Two resistances of $10\Omega$ each are connected in series with X and Y separately. The balance point is 45 cm. The value of X and Y are

• A. $12\Omega ,8\Omega$
• B. $4\Omega ,6\Omega$
• C. $8\Omega ,12\Omega$
• D. $12\Omega ,16\Omega$

Answer 1

The correct option is C $8\Omega ,12\Omega$

$\frac{x}{y}=\frac{40}{100-40}=\frac{40}{60}=\frac{2}{3}\to \left(1\right)\frac{x+10}{y+10}=\frac{45}{55}=\frac{9}{11}\frac{\frac{2}{3}y+10}{y+10}=\frac{9}{11}\frac{2}{3}\times 11y+110=9y+9020=9y-\frac{22}{3}y20\times 3=5yy=12\Omega x=\frac{2}{3}\times 12=8\Omega$