Series Combination of Cells

Q. Two cells of emf $2E$ and $E$ with internal resistance $r_1$ and $r_2$ respectively are connected in series to an external resistor $R$ (see figure). The value of $R$, at which the potential difference across the terminals of the first cell becomes zero is

1. $r_1-r_2$
2. $r_1+r_2$
3. $\frac{r_1}{2}+r_2$
   
4. $\frac{r_1}{2}-r_2$
   

Q. 24 cells of each emf 4V are connected in series. Among them if 5 cells are connected wrongly, the effective emf of the combination is

1. 18V
2. 56V
3. 24V
4. 4V

Q.

Which of the following statements is correct about the circuit shown in figure where 1 ohm and 0.5 ohm are the internal resistances of the 6 V and 12 V batteries respectively?

1. If a voltmeter is connected across the 6 V battery it will read 5 V
2. The potential at point Q is +0.5 V
3. The potential at point P is 6 V
4. If a voltmeter is connected across the 6 V battery it will read 7 V

Q. A wire of length L and 3 identical cells of negligible internal resistances are connected in series. Due to this current, the temperature of the wire is raised by $\Delta T$ in time t. A number N of similar cells is now connected in series with a wire of the same material and cross-section but of length 2L. The temperature of wire is raised by same amount $\Delta T$ in the same time t. The value of N is

1. 8
2. 9
3. 4
4. 6

Q. The magnitude and direction of the current in the circuit shown will be

1. 1.0 A from b to a through e
2. 1.0 A from a to b through e
3. $\frac{7}{3}$ A from a to b through e
4. $\frac{7}{3}$ A from b and a through e

Q. Find the current through 4 $\Omega$ resistor in the circuit shown.

1. $0A$
2. $\frac{6}{19}A$
3. $\frac{19}{6}A$
4. $0.4A$

Q. Two batteries A and B each of emf 2 volt are connected in series to external resistance $R=1\Omega$. Internal resistance of A and B are $1.9\Omega$ and $0.9\Omega$ respectively. What is the potential difference between the terminals of battery A ?

1. 2 V
2. 3.8 V
3. 0
4. None of these

Q. In a mixed grouping of identical cells 5 rows are connected in parallel and each row contains 10 cells. This combination send a current i through an external resistance of $20\Omega$. If the emf and internal resistance of each cell is 1.5 volt and $1\Omega$ respectively then the value of i is

1. 0.14 A
2. 0.25 A
3. 0.75 A
4. 0.68 A

Q. A group of N cells whose emf varies directly with the internal resistance as per the equation $E_N=1.5r_N$ are connected as shown in the following figure. The current i in the circuit is

1. 0.51 amp
2. 5.1 amp
3. 0.15 amp
4. 1.5 amp

Q. With reference to the circuit as shown in figure, what is the current maintained?

1. 1.5A
2. 15A
3. 0.67A
4. 6.67A