Two cells, having the same $e.m.f.$ are connected in series through an external resistance $R.$ Cells have internal resistances $r_1$ and $r_2\,\, (r_1 > r_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of $R$ is
  • A$\sqrt {{r_1}{r_2}} $
  • B$\;{r_1} + {r_2}$
  • C$\;{r_1} - {r_2}$
  • D$\frac{{\;{r_1} + {r_2}}}{2}$
AIPMT 2006,JEE MAIN 2022, Medium
art

Download our app
and 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

  • 1
    In $n_e$ and $v_d$ be the number of electrons and drift velocity in a semiconductor. When the temperature is increased
    View Solution
  • 2
    Figure shows three resistor configurations $R_1,R_2$ and $R_3$ connected to $3\,V$ battery. If the power dissipated by the configuration $R_1, R_2$ and $R_3$ is $P_1, P_2$ and $P_3$ , respectively then
    View Solution
  • 3
    If each resistance in the figure is of $9\,\Omega$ then reading of ammeter is ............ $A$
    View Solution
  • 4
    The figure shows a circuit having eight resistances of $1 \Omega$ each, labelled $R_1$ to $R_8$, and two ideal batteries with voltages $\varepsilon_1=12 V$ and $\varepsilon_2=6 V$.

    Which of the following statement($s$) is(are) correct?

    $(A)$ The magnitude of current flowing through $R_1$ is $7.2 A$.

    $(B)$ The magnitude of current flowing through $R_2$ is $1.2 A$.

    $(C)$ The magnitude of current flowing through $R_3$ is $4.8 A$.

    $(D)$ The magnitude of current flowing through $R_5$ is $2.4 A$.

    View Solution
  • 5
    In a hydrogen discharge tube it is observed that through a given cross-section $3.13 \times {10^{15}}$ electrons are moving from right to left and $3.12 \times {10^{15}}$ protons are moving from left to right. What is the electric current in the discharge tube and what is its direction
    View Solution
  • 6
    Two electric bulbs whose resistance are in the ratio of $1: 2$, are connected in parallel to a constant voltage source. The power dissipated in them has the ratio
    View Solution
  • 7
    The effective resistance between points $P$ and $Q$ of the electrical circuit shown in the figure is
    View Solution
  • 8
    The resistance in the two arms of a meter bridge are $5\,\Omega $ and $R\,\Omega $, respectively. When the resistance $R$ is shunted with an equal resistance, the new balance point is at $1.6\, l_1$. The resistance $‘R’$ is ................. $\Omega$
    View Solution
  • 9
    The resistance of a wire is $R$. It is bent at the middle by $180^o$ and both the ends are twisted together to make a shorter wire. The resistance of the new wire is
    View Solution
  • 10
    Water boils in an electric kettle in $15\,\min$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value, then the same amount of water will boil with the same supply voltage in ............. $min$
    View Solution