$\mathrm{Two} \mathrm{battries} \mathrm{of} \mathrm{emf} {\mathrm{E}}_1, {\mathrm{E}}_2 \mathrm{and} \mathrm{internal} \mathrm{resistance} {\mathrm{r}}_1, {\mathrm{r}}_2 \mathrm{are} \mathrm{connected} in parallel.$
$\mathrm{The} \mathrm{effective} \mathrm{emf} \mathrm{of} \mathrm{the} \mathrm{circuit} \mathrm{across} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{is}$

1.  $\frac{{\mathrm{E}}_1{\mathrm{r}}_1 + {\mathrm{E}}_2{\mathrm{r}}_2}{{\mathrm{r}}_1 + {\mathrm{r}}_2}$

2.  $\frac{{\mathrm{E}}_1{\mathrm{r}}_2 + {\mathrm{E}}_2{\mathrm{r}}_1}{{\mathrm{r}}_1 + {\mathrm{r}}_2}$

3.  $\frac{{\mathrm{E}}_1{\mathrm{r}}_2 + {\mathrm{E}}_2{\mathrm{r}}_1}{{\mathrm{r}}_1 \times {\mathrm{r}}_2}$

4.  $\frac{{\mathrm{E}}_1{\mathrm{r}}_1 + {\mathrm{E}}_2{\mathrm{r}}_2}{{\mathrm{r}}_1 - {\mathrm{r}}_2}$

The equivalent resistance across AB is :

1.  2R

2.  R/2

3.  4R/3

4.  3R/2

The equivalent resistance between points \(A\) and \(B\) in the circuit shown in the figure is:

In the circuit shown in the figure, the effective resistance between A and B is:

1.  2$\mathrm{\Omega }$

2.  4$\mathrm{\Omega }$

3.  6$\mathrm{\Omega }$

4.  8$\mathrm{\Omega }$

For the circuit shown in the figure, the value of R must be

1.  3$\mathrm{\Omega }$

2.  4$\mathrm{\Omega }$

3.  5$\mathrm{\Omega }$

4.  6$\mathrm{\Omega }$

Current I as shown in the circuit will be

1.  10 A

2.  $\frac{20}{3} \mathrm{A}$

3.  $\frac{2}{3} \mathrm{A}$

4.  $\frac{5}{3} \mathrm{A}$

The current through the 5$\mathrm{\Omega }$ resistor is

(1) 3.2A                     

(2) 2.8A

(3) 0.8A                     

(4) 0.2A

In the figure, a carbon resistor has bands of different colours on its body as mentioned in the figure. The value of the resistance is:

 
1. \(2.2\) k\(\Omega\)
2. \(3.3\) k\(\Omega\)
3. \(5.6\) k\(\Omega\)
4. \(9.1\) k\(\Omega\)

A copper wire has a square cross-section, 2.0 mm on a side. It carries a current of 8 A and the density of free electrons is 8 × 10²⁸ m^–3. The drift speed of electrons is equal to 

(1) 0.156 × 10^–3 m.s^–1

(2) 0.156 × 10^–2 m.s^–1

(3) 3.12 × 10^–3 m.s^–1

(4) 3.12 × 10^–2 m.s^–1

The equivalent resistance of the following infinite network of resistances is 

(1) Less than 4 Ω

(2) 4 Ω

(3) More than 4 Ω but less than 12 Ω

(4) 12 Ω