12 cells,each having the same emf E and inter | vedclass

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

Question

(B) Let $n$ be the number of wrongly connected cells.Number of cells helping = $(12 - n)$.Number of cells opposing = $n$.Resultant $emf$ of the $12$ c

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Let $n$ be the number of wrongly connected cells.Number of cells helping = $(12 - n)$.Number of cells opposing = $n$.Resultant $emf$ of the $12$ cells = $(12 - n)E - nE = (12 - 2n)E$.Total resistance of the $12$ cells = $12r$.When the two additional cells aid the battery,the total $emf$ is $(12 - 2n)E + 2E = (14 - 2n)E$ and total resistance is $14r$.Given current $I_1 = 3 \, A$,so $\frac{(14 - 2n)E}{14r} = 3$  --- $(i)$.When the two additional cells oppose the battery,the total $emf$ is $(12 - 2n)E - 2E = (10 - 2n)E$ and total resistance is $14r$.Given current $I_2 = 2 \, A$,so $\frac{(10 - 2n)E}{14r} = 2$  --- $(ii)$.Dividing $(i)$ by $(ii)$:$\frac{14 - 2n}{10 - 2n} = \frac{3}{2}$$28 - 4n = 30 - 6n$$2n = 2 \implies n = 1$.Thus,the number of wrongly connected cells is $1$.

Similar Questions

Two cells of emf $E_{1}$ and $E_{2}$ are joined in opposition (such that $E_{1} > E_{2}$). If $r_{1}$ and $r_{2}$ are the internal resistances and $R$ is the external resistance,then the terminal potential difference across the external resistance $R$ is:

When a current of $2 \ A$ flows through a resistor of $2 \ \Omega$,the terminal voltage across the cell is $E/2$. The internal resistance of the cell is ........ $\Omega$.

Two sources of equal $emf$ $(\varepsilon)$ are connected in series to an external resistance $R$. The internal resistances of the two sources are $R_1$ and $R_2$ $(R_2 > R_1)$. If the potential difference across the source having internal resistance $R_2$ is zero, then:

When a battery is connected across a resistor of $16 \Omega$,the voltage across the resistor is $12 \ V$. When the same battery is connected across a resistor of $10 \Omega$,the voltage across it is $11 \ V$. The internal resistance of the battery in ohm is

The internal resistance of a cell is the resistance of

Vedclass Test Series

Exam Paper Generator

Online Exam Module