$12$ 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
Diffcult
Download our app for free and get started
(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$$ = (12 - 2n)E$
Total resistance of cells = $12r$
( resistance remains same irrespective of connections of cells)
With additional cells
$(a)$ Total $e.m.f.$ of cells when additional cells help battery =$ (12 -2n) E + 2E$
Total resistance = $12r + 2r = 14r$
$\frac{{(12 - 2n)E + 2E}}{{14r}} = 3$ ......$(i)$
$(b)$ Similarly when additional cells oppose the battery
$\frac{{(12 - 2n)E - 2E}}{{14r}} = 2$......$(ii)$
Solving $(i)$ and $(ii)$, $n = 1$
Number of cells helping one another $ = (12 - n)$
Total $e.m.f.$ of such cells $ = (12 - n)E$
Total $e.m.f.$ of cells opposing = $nE$
Resultant $e.m.f.$ of battery $ = (12 - n)E - nE$$ = (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 $(ii)$, $n = 1$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1In the figure shown, battery $1$ has $\mathrm{emf}$ $= 6\, V$ and internal resistance $= 1 \,\Omega$. Battery $2$ has $\mathrm{emf}$ $= 2\,V$ and internal resistance $= 3\, \Omega$ . The wires have negligible resistance. What is the potential difference across the terminals of battery $2$ ? ................ $V$View Solution
- 2The resistance of a heater coil is $110\, ohm$. A resistance $R$ is connected in parallel with it and the combination is joined in series with a resistance of $11\, ohm$ to a $220\, volt$ main line. The heater operates with a power of $110\, watt$. The value of $R$ in $ohm$ isView Solution
- 3When two resistance are connected in parallel then the equivalent resistance is $\frac {6}{5}\Omega $ . When one of the resistance is removed then the effective resistance is $2\, \Omega $. The resistance of the wire removed will be ................ $\Omega$View Solution
- 4An electric kettle has two coils. When one of these is switched on, the water in the kettle boils in $6\,\min$ . When the other coil is switched on, the water boils in $3\,\min$. If the two coils are connected in series, the time taken to boil the water in the kettle is ............. $min$View Solution
- 5The voltage $V$ and current $I$ graph for a conductor at two different temperatures ${T_1}$ and ${T_2}$ are shown in the figure. The relation between ${T_1}$ and ${T_2}$ isView Solution
- 6Four lamps are connected in the way shown in the figure. When switch $S_2$ is open and switch $S_1$ is on position $-2$ , lamp $-b$ is the brightest, and lamp $-c$ and lamp $-d$ are the dimmest and are of the same brightness. Now $S_2$ is closed and $S_1$ is on position $-1$ , the sequence in brightness of the lamps is (with the first in the sequence being the brightest)View Solution
- 7Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance $2000 \,\Omega$ is used to measure the potential difference across $500 \,\Omega$ resister, the reading of the voltmeter will be ............... $V$View Solution
- 8View SolutionConsider four circuits shown in the figure below. In which circuit power dissipated is greatest (Neglect the internal resistance of the power supply)
- 9A uniform metallic wire carries a current $2\,A$. when $3.4\,V$ battery is connected across it. The mass of uniform metallic wire is $8.92 \times 10^{-3} \,kg$. density is $8.92 \times 10^3\,kg / m ^3$ and resistivity is $1.7 \times 10^{-8} \Omega- m$. The length of wire is $l=............\,m$View Solution
- 10View SolutionWhich is a wrong statement