In a meter bridge,the wire of length 1, m has | vedclass

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

Question

(C) Given $\frac{dR}{d\ell} = \frac{k}{\sqrt{\ell}}$,where $k$ is a constant.Integrating from $\ell = 0$ to $\ell = 1\, m$,the total resistance $R_{AB

Vedclass · Accepted Answer

$0.25$

Vedclass · Answer

(C) Given $\frac{dR}{d\ell} = \frac{k}{\sqrt{\ell}}$,where $k$ is a constant.Integrating from $\ell = 0$ to $\ell = 1\, m$,the total resistance $R_{AB}$ of the wire is:$R_{AB} = \int_{0}^{1} \frac{k}{\sqrt{\ell}} d\ell = k [2\sqrt{\ell}]_{0}^{1} = 2k$.Let the length $AP = L$. The resistance of segment $AP$ is $R_{AP} = \int_{0}^{L} \frac{k}{\sqrt{\ell}} d\ell = k [2\sqrt{\ell}]_{0}^{L} = 2k\sqrt{L}$.The resistance of segment $PB$ is $R_{PB} = \int_{L}^{1} \frac{k}{\sqrt{\ell}} d\ell = k [2\sqrt{\ell}]_{L}^{1} = 2k(1 - \sqrt{L})$.For a balanced meter bridge with equal resistances $R'$ in the gaps,the condition is $\frac{R'}{R_{AP}} = \frac{R'}{R_{PB}}$,which implies $R_{AP} = R_{PB}$.Therefore,$2k\sqrt{L} = 2k(1 - \sqrt{L})$.$\sqrt{L} = 1 - \sqrt{L} \implies 2\sqrt{L} = 1 \implies \sqrt{L} = 0.5$.$L = (0.5)^2 = 0.25\, m$.

Similar Questions

$A$ balanced bridge is shown in the circuit diagram. The metre bridge wire has a resistance of $1 \Omega \text{ cm}^{-1}$. The current drawn from the battery is (Internal resistance of the battery is negligible). (in $\text{ A}$)

In a meter bridge,the null point is found at a distance of $25\, cm$ from $A$. If now a resistance of $10\,\Omega$ is connected in parallel with $S$,the null point occurs at the midpoint of $AB$. The value of $R$ is ................. $\Omega$. (in $.67$)

During an experiment with a meter bridge,the galvanometer shows a null point when the jockey is pressed at $40.0 \ cm$ using a standard resistance of $90 \ \Omega$,as shown in the figure. The least count of the scale used in the meter bridge is $1 \ mm$. The unknown resistance is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module