$12$ cells each having the same emf are connected in series and are kept in a closed box. Some of the cells are wrongly connected. This battery is connected in series with an ammeter and two cells identical with each other and also identical with the previous cells. The current is $3\, A$ when the external cells aid this battery and is $2\,A$ when the cells oppose the battery. How many cells in the battery are wrongly connected :-
Diffcult
Download our app for free and get started
Assume $\mathrm{M}$ cells are connected correct and $\mathrm{N}$ cells connected wrong.
$\mathrm{M}+\mathrm{N}=12$ ............$(1)$
$(M+2) E-N E=3 R \Rightarrow M-N+2=\frac{3 R}{E}$ ..........$(2)$
$\mathrm{ME}-(\mathrm{N}+2) \mathrm{E}=2 \mathrm{R} \quad \Rightarrow \mathrm{M}-\mathrm{N}-2=\frac{2 \mathrm{R}}{\mathrm{E}}$ ...........$(3)$
from eq $(1)$ and $(2)$
$-\mathrm{M}+\mathrm{N}+10=0 \quad \Rightarrow \mathrm{M}-\mathrm{N}=10$ .........$(4)$
$\mathrm{M}=11, \mathrm{N}=1$
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
- 1Two electric lamps of $40\, watt$ each are connected in parallel. The power consumed by the combination will be ........... $watt$View Solution
- 2The equivalent resistance betweent point $A$ and $B$View Solution
- 3A current source drives a current in a coil of resistance $R_1$ for a time $t$. The same source drives current in another coil of resistance $R_2$ for same time. If heat generated is same, find internal resistance of source.View Solution
- 4If power in external resistance $R$ is maximum thenView Solution
$(i) R = r$ $(ii)$ Power in $R$ is $\frac{{{E^2}}}{{4R}}$
$(iii)$ Input power $\frac{{{E^2}}}{{2R}}$ $(iv)$Efficiency is $50\%$
- 5In the adjoining circuit shown the potential difference between points $A$ and $B$ will beView Solution
- 6What will be equivalent resistance of circuit between $x$ and $y$View Solution
- 7Two light bulbs in the circuit have rating $A\,[24\ V, 48\,W]$ and $B\,[24\ V, 36\,W]$ as shown.View Solution
- 8Two current elements $P$ and $Q$ have current voltage characteristics as shown below :View Solution
Which of the graphs given below represents current voltage characteristics when $P$ and $Q$ are in series.
- 9In the circuit shown, what is the potential difference $V_{PQ}$? ................ $V$View Solution
- 10Figure shows a thick shell made of electrical conductivity $\sigma$ and has inner & outer radii of $10\ cm$ & $20\ cm$ respectively and is filled with ice inside it. Its inside and outside surface are kept at different potentials by a battery of internal resistance $\frac{2}{\pi} \Omega \ \&\ \in = 5V$. Find value of $\sigma$ for which ice melts at maximum possible rate if $25\%$ of heat generated by shell due to joule heating is used to melt ice.View Solution
