Two cells of internal resistance r_{1} and r_ | vedclass

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

Question

(C) Since the two cells are connected in series,the total emf is $E_{total} = E + E = 2E$,where $E$ is the emf of each cell.The total resistance of th

Vedclass · Accepted Answer

$R=r_{1}-r_{2}$

Vedclass · Answer

(C) Since the two cells are connected in series,the total emf is $E_{total} = E + E = 2E$,where $E$ is the emf of each cell.The total resistance of the circuit is $R_{total} = R + r_{1} + r_{2}$.The current $I$ flowing through the circuit is given by $I = \frac{2E}{R + r_{1} + r_{2}}$.The terminal potential difference $V_{1}$ across the cell with internal resistance $r_{1}$ is given by $V_{1} = E - Ir_{1}$.Given that $V_{1} = 0$,we have $E - Ir_{1} = 0$,which implies $E = Ir_{1}$.Substituting the value of $I$,we get $E = \left( \frac{2E}{R + r_{1} + r_{2}} \right) r_{1}$.Dividing both sides by $E$,we get $1 = \frac{2r_{1}}{R + r_{1} + r_{2}}$.Rearranging the terms,$R + r_{1} + r_{2} = 2r_{1}$.Therefore,$R = 2r_{1} - r_{1} - r_{2} = r_{1} - r_{2}$.

Two cells of internal resistance $r_{1}$ and $r_{2}$ and of the same emf are connected in series across a resistor of resistance $R$. If the terminal potential difference across the cell of internal resistance $r_{1}$ is zero,then the value of $R$ is

Similar Questions

$10$ identical cells,each of potential $E$ and internal resistance $r$,are connected in series to form a closed circuit. What is the potential difference across any $3$ cells (in $E$)?

Four identical cells,each having an electromotive force $(e.m.f.)$ of $12\,V$,are connected in parallel. The resultant electromotive force $(e.m.f.)$ of the combination is .............. $V$.

Two identical cells each of emf $E$ and internal resistance $r$ are connected in parallel with an external resistance $R$. To get maximum power developed across $R$, the value of $R$ is

The circuit in the figure shows two cells connected in opposition to each other. Cell $E_1$ has an $emf$ of $6 \ V$ and an internal resistance of $2 \ \Omega$. Cell $E_2$ has an $emf$ of $4 \ V$ and an internal resistance of $8 \ \Omega$. Find the potential difference between the points $A$ and $B$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module