Question

A resistance of $2\Omega$ is connected across one gap of a metrebridge ( the length of the wire is 100 cm) and an unknown resistance, greater than $2\Omega$ , is connected across the other gap. When these resistance's are interchanged, the balance point shifts by 20cm. Neglecting any corrections, the unknown resistance is:

• A. $3\Omega$
• B. $4\Omega$
• C. $5\Omega$
• D. $6\Omega$

Answer 1

The correct option is A $3\Omega$

Given: A resistance of 2Ω is connected across one gap of a metre bridge ( the length of the wire is 100 cm) and an unknown resistance, greater than 2Ω , is connected across the other gap. When these resistance's are interchanged, the balance point shifts by $20cm$

To find the unknown resistance

Solution:

Given, $R=2\Omega$

From the first condition given,

$\frac{R}{x}=\frac{l}{100-l}⟹x=\frac{2(100-l)}{l}.......\left(i\right)$

Now, from second condition given,

$\frac{x}{R}=\frac{l+20}{80-l}....\left(ii\right)$

Put the value of $x$ from equation (i) in (ii)

$⟹\frac{2(100-l)}{2l}=\frac{l+20}{80-l}⟹(100-l)(80-l)=l(l+20)⟹8000-100l-80l+l^2=l^2+20l⟹8000-=20l+180l⟹l=\frac{8000}{200}=40cm$

Put this value in equation (ii),

$x=\frac{2\times (40+20)}{80-40}⟹x=\frac{2\times 60}{40}⟹x=3\Omega$

is the value of unknown resistance.