Parallel Combination of Cells

Q. Find the current through $2\text{V}$ battery.

1. $4\text{A}$
2. $2\text{A}$
3. $1\text{A}$
4. $3\text{A}$

Q. In the circuit shown below $E_1=4.0V,R_1=2\Omega ,E_2=6.0V,R_2=4\Omega$ and $R_3=2\Omega$. The current $I_1$is

1. 1.6 A
2. 1.8 A
3. 1.25 A
4. 1.0 A

Q. In the circuit shown here $E_1=E_2=E_3=2V$ and $R_1=R_2=4\Omega$. The current flowing between point A and B through battery $E_2$ is

1. Zero
2. 2 A from A to B
3. 2 A from B to A
4. None of these

Q. Two identical parallel-plate capacitors are connected in series and then joined across a battery of 100 V. A slab of dielectric constant K = 3 is inserted between the plates of the first capacitor. Then, the potential difference across the capacitors will respectively be

1. 25 V, 75 V
2. 75 V, 25 V
3. 20 V, 80 V
4. 50 V, 50 V

Q. For the batteries shown in the figure, $R_1,R_2,$ and $R_3$ are the internal resistances of $E_1,E_2,$ and $E_3$ respectively. Then, which of the following is/are correct?

1. The equivalent internal resistance $R$ of the system is given by $\frac{\left(R_1{R}_2{R}_3\right)}{(R_1{R}_2+R_2{R}_3+R_3{R}_1).}$
2. If $E_3=\frac{(E_1{R}_2+E_2{R}_1)}{(R_1+R_2)}$, the equivalent emf of the batteries will be equal to $E_3$.
3. The equivalent e.m.f. of the battery is equal to
   $=\frac{E_1+E_2+E_3}{3}$
4. The equivalent e.m.f. of the battery not only depends upon values of $E_1,E_2$ and $E_3$ but also depends upon values of $R_1,R_2$ and $R_3$.

Q. Two non-ideal batteries are connected in parallel. The equivalent EMF is smaller than either of the two EMFs?

1. True
2. False

Q. In the circuit shown here $E_1=E_2=E_3=2V$ and $R_1=R_2=4\Omega$. The current flowing between point A and B through battery $E_2$ is

1. Zero
2. 2 A from A to B
3. 2 A from B to A
4. None of these

Q.

A single battery fo emf E and internal resistance r is equivalent to a parallel combination of two batteries of emfs $E_1=2V$ and $E_2=1.5V$ and internal resistances $r_1=1\Omega$ and $r_2=2\Omega$ respectively, with polarities as shown in the figure.

(IIT-JEE 1997)

1. $E=\frac{5}{6}V$

2. E = 1.2 V

3. r = 1.5 Ω

4. $r=\frac{2}{3}\Omega$

Q. Find the current through the resistor B in the given circuit. Each resistor has a resistance of $10\Omega$ and each battery has an EMF of 10 V.

1. 0A
2. 1A
3. 10A
4. 0.1A

Q. If two non-ideal batteries are connected in parallel, the equivalent EMF is smaller than either of the two EMFs.

1. True
2. False