SATHEE: current-electricity Question 54

current-electricity Question 54

Question: Q. 7. In the given circuit, a metre bridge is shown in the balanced state. The metre bridge vire has a resistance of $1 Ω {cm}^{- 1}$ . Calculate the unknown resistance $X$ and the current drawn from the battery of a negligible internal resistance if the magnitude of $Y$ is $6 Ω$ . If at the balancing point, we interchange the position of galvanometer and the cell, how it will affect the position of the galvanometer?

A&E [CBSE SQP, 2016]

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Solution:

Ans. } \quad $\begin{aligned} \frac{X}{Y} & = \frac{40}{60} = \frac{2}{3} X & = 4 Ω . \end{aligned}$ $$

$4 Ω$ and $6 Ω$ are in series, $= 10 Ω$

$40 Ω$ and $60 Ω$ are in series, $= 100 Ω$

$10 Ω$ and $100 Ω$ are in parallel, $= \frac{1000}{110} Ω = 9.09 Ω 1$

There will be no change in the balancing length. $1 / 2$ Formulae for series and parallel :

For parallel

$R^{'} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}$

For series

$R^{'} = R_{1} + R_{2}$

[CBSE Marking Scheme 2016]

[AI Q. 8.In the figure a long uniform potentiometer wire $A B$ is having a constant potential gradient along its length. The null points for the two primary cells of emf $E_{1}$ and $E_{2}$ connected in the manner shown are obtained at a distance of $120 cm$ and $300 cm$ from the end $A$ . Find (i) $E_{1} / E_{2}$ and (ii) position of null point for the cell $E_{1}$ .

How is the sensitivity of a potentiometer increased?

A [Delhi I, II, III 2012]

Ans. (i) $E_{1} + E_{2} = 300 K$

( $K$ is potential gradient in volt $/ cm$ )

$\Rightarrow \frac{E_{1}}{E_{2}} = \frac{7}{3}$

(ii)

$\begin{aligned} E_{1} + E_{2} & = 300 K E_{1} + \frac{3}{7} E_{1} & = 300 K \end{aligned}$

$\Rightarrow E_{1} = 210 K$

Therefore, balancing length for cell $E_{1}$ is $210 cm . \frac{1 / 2}{2}$ (Award this $1 / 2$ mark even if the student writes $E_{1} = 240 K)$

(Award full marks for any other correct method)

By decreasing potential gradient, the sensitivity of a potentiometer is increased.

[Or through increasing length, reducing potential drop across wire, increasing resistance input in series with the main cell etc.]

[CBSE Marking Scheme 2012]

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Current Electricity

current-electricity Question 54

Table of Contents

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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