Question

The resistances in the two arms of the meter bridge are $5\Omega andR\Omega$, respectively. When the resistance R is shunted with an equal resistance, the new balance point is at 1.6, the resistance R is

• A. $10\Omega$
• B. $15\Omega$
• C. $20\Omega$
• D. $25\Omega$

Answer 1

The correct option is B

$15\Omega$

Case - 1
$\frac{5}{R}=\frac{{\ell }_1}{100-{\ell }_1}$ .....(1)
Case-2
When R is shunted with an equal resistance R, shunt placed parallel to R.
$\frac{5}{\frac{R}{2}}=\frac{1.6{\ell }_1}{100-1.6{\ell }_1}.....\left(2\right)$
By (1) and (2)
$2[100-1.6{\ell }_1]=1.6[100-{\ell }_1]200-3.2{\ell }_1=160-1.6{\ell }_{1}40=1.6{\ell }_1{\ell }_1=25cm{\ell }_1=25cm$
Put this in (1)
$\frac{5}{R}=\frac{25}{75}R=15\Omega$