12 cells each having same emf are connected in series with some c… - Vidyadip

MCQ

$12$ cells each having same $emf$ are connected in series with some cells wrongly connected. The arrangement is connected in series with an ammeter and two cells which are in series. Current is $3 \,A$ when cells and battery aid each other and is $2\, A$ when cells and battery oppose each other. The number of cells wrongly connected is

A
$4$
✓
$1$
C
$3$
D
$2$

✓

Answer

Correct option: B.

$1$

b
(b) Let $n$ be the number of wrongly connected cells.
Number of cells helping one another $ = (12 - n)$
Total $e.m.f.$ of such cells $ = (12 - n)E$
Total $e.m.f.$ of cells opposing = $nE$
Resultant $e.m.f.$ of battery $ = (12 - n)E - nE$$ = (12 - 2n)E$
Total resistance of cells = $12r$
( resistance remains same irrespective of connections of cells)
With additional cells
$(a)$ Total $e.m.f.$ of cells when additional cells help battery =$ (12 -2n) E + 2E$
Total resistance = $12r + 2r = 14r$
$\frac{{(12 - 2n)E + 2E}}{{14r}} = 3$ ......$(i)$
$(b)$ Similarly when additional cells oppose the battery
$\frac{{(12 - 2n)E - 2E}}{{14r}} = 2$......$(ii)$
Solving $(i)$ and $(ii)$, $n = 1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Two charges of $4\,\mu C$ each are placed at the corners $A$ and $B $ of an equilateral triangle of side length $0.2\, m $ in air. The electric potential at $C$ is $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N{\rm{ - }}{m^2}}}{{{C^2}}}} \right]$

A radioactive substance emits

Two wires of copper having the length in the ratio $4 : 1$ and their radii ratio as $1 : 4$ are stretched by the same force. The ratio of longitudinal strain in the two will be

Select the correct alternative

An astronomical refracting telescope is being used by an observer to observe planets in normal adjustment. The focal lengths of the objective and eye piece used in the construction of the telescope are $20\,m$ and $2\,cm$ respectively. Consider the following statements about the telescope :

$(a)$ The distance between the objective and eye piece is $20.02\; m$

$(b)$ The magnification of the telescope is $1000$

$(c)$ The image of the planet is erect and diminished

$(d)$ The aperture of eye piece is smaller than that of objective

The correct statements are :

The root mean square speed of molecules of a given mass of a gas at $27^{\circ} C$ and $1$ atmosphere pressure is $200\, ms ^{-1}$. The root mean square speed of molecules of the gas at $127^{\circ} C$ and $2$ atmosphere pressure is $\frac{ x }{\sqrt{3}}\, ms ^{-1} .$ The value of $x$ will be ......$ms ^{-1} .$

A particle describes a horizontal circle of radius $r$ on the smooth surface of an inverted cone as shown. The height of plane of circle above vertex is $h$. The speed of particle should be

The diagram showing the variation of gravitational potential of earth with distance from the centre of earth is

Which of the following statements is not true ? In the case of a simple pendulum for small amplitudes the period of oscillation is

At what temperature the centigrade (Celsius) and Fahrenheit, readings are the same ........ $^o$