A resistance of 2,Omega is connected across o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the unknown resistance be $X$. In a meter bridge,the balance condition is given by $\frac{R}{X} = \frac{\ell}{100-\ell}$,where $\ell$ is the b

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Let the unknown resistance be $X$. In a meter bridge,the balance condition is given by $\frac{R}{X} = \frac{\ell}{100-\ell}$,where $\ell$ is the balance length in $cm$.Initially,$\frac{2}{X} = \frac{\ell}{100-\ell} \implies X = \frac{2(100-\ell)}{\ell} \quad (1)$Since $X > 2$,the balance point shifts when resistances are interchanged. The new balance condition is $\frac{X}{2} = \frac{\ell+20}{100-(\ell+20)} = \frac{\ell+20}{80-\ell} \quad (2)$Substituting $X$ from $(1)$ into $(2)$:$\frac{2(100-\ell)}{\ell} \cdot \frac{1}{2} = \frac{\ell+20}{80-\ell}$$\frac{100-\ell}{\ell} = \frac{\ell+20}{80-\ell}$$(100-\ell)(80-\ell) = \ell(\ell+20)$$8000 - 100\ell - 80\ell + \ell^2 = \ell^2 + 20\ell$$8000 = 200\ell \implies \ell = 40\,cm$Now,substitute $\ell = 40$ into equation $(1)$:$X = \frac{2(100-40)}{40} = \frac{2 	imes 60}{40} = 3\,\Omega$.

Similar Questions

In a meter bridge experiment,the ratio of the left gap resistance to the right gap resistance is $2:3$. The balance length from the left end is (in $\,cm$)

In the given Wheatstone bridge (meter bridge) circuit,the galvanometer shows zero deflection. The value of the unknown resistance $R$ is ................. $\Omega$.

In the given arrangement of the experiment on a meter bridge,if $AD$ corresponding to the null deflection of the galvanometer is $X$,what would be its value if the radius of the wire $AB$ is doubled?

The figure shows a meter-bridge circuit,with $AB = 100\, cm$,$X = 12\,\Omega$ and $R = 18\,\Omega$,and the jockey $J$ in the position of balance. If $R$ is now made $8\,\Omega$,through what distance will $J$ have to be moved to obtain balance? .............. $cm$

Vedclass Test Series

Exam Paper Generator

Online Exam Module