A cell can be balanced against 110 cm and 100 cm of the potentiometer wire, respectively with and without being short circuited through a resistance of $10\mathrm{\Omega }$. Its internal resistance is

1. zero

2. $1.0\mathrm{\Omega }$

3. $0.5\mathrm{\Omega }$

4. $2.0\mathrm{\Omega }$

A wire of resistance 12  $\mathrm{\Omega }$ is bent to form a complete circle of radius 10 cm. The resistance between its two diametrically opposite points, A and B as shown in the figure is

1. $3\mathrm{\Omega }$

2. $6\mathrm{\pi \Omega }$

3. $6\mathrm{\Omega }$

4. $0.6\mathrm{\pi \Omega }$

See the electrical circuit shown in the figure below. Which of the following equations is a correct equation for it?

1.${\mathrm{\epsilon }}_2-{\mathrm{i}}_2{\mathrm{r}}_2-{\mathrm{\epsilon }}_1+{\mathrm{i}}_1{\mathrm{r}}_1=0$

2. $-{\mathrm{\epsilon }}_2-({\mathrm{i}}_1+{\mathrm{i}}_2)\mathrm{R}+{\mathrm{i}}_2{\mathrm{r}}_2=0$

3. ${\mathrm{\epsilon }}_1-({\mathrm{i}}_1+{\mathrm{i}}_2)\mathrm{R}+{\mathrm{i}}_1{\mathrm{r}}_1=0$

4. ${\mathrm{\epsilon }}_1+({\mathrm{i}}_1+{\mathrm{i}}_2)\mathrm{R}-{\mathrm{i}}_1{\mathrm{r}}_1=0$

If the power dissipated in the $9\mathrm{\Omega }$ resistor in the circuit shown is 36 W, the potential difference across the $2\mathrm{\Omega }$ resistor is

1. 2V

2. 4V

3. 8V

4. 10V

An electric kettle takes 4A current at 220 V. How much time will it take to boil 1kg of water from temperature $20°\mathrm{C}$? The temperature of boiling water is $100°\mathrm{C}$ .

1. 4.2 min

2. 6.3 min

3. 8.3 min

4. 12.6 min

The total power dissipated in Watts in the circuit shown here is

1. 4

2. 16

3. 30

4. 54

Two cells, having the same emf, are connected in series through an external resistance R. Cells have internal resistances ${\mathrm{r}}_1$ and ${\mathrm{r}}_2({\mathrm{r}}_1>{\mathrm{r}}_2)$ respectively. When the circuit is closed, the potential difference across the first cell is zero. The value of R is

1. ${\mathrm{r}}_1-{\mathrm{r}}_2$

2. $\frac{r_1+r_2}{2}$

3. $\frac{r_1-r_2}{2}$

4. $r_1+r_2$

For the network shown in the figure, the value of the current i is

1. $\frac{18V}{5}$

2. $\frac{5V}{9}$

3. $\frac{9V}{35}$

4. $\frac{5V}{18}$

Two batteries, one of emf 18 V and internal resistance $2\mathrm{\Omega }$ and the other of emf 12 V and internal resistance $1\mathrm{\Omega }$, are connected as shown. The voltmeter V will record a reading of

1. 18 V

2. 30 V

3. 14 V

4. 15 V

Five equal resistances each of resistance R are connected as shown in the figure. A battery of V volts is connected between A and B. The current flowing in AFCEB will be

1. $\frac{V}{R}$

2. $\frac{V}{2R}$

3. $\frac{2V}{R}$

4. $\frac{3V}{R}$