A battery of internal resistance \(r\), when connected across \(2~\Omega\) resistor supplies a current of \(4~\text{A}\). When the battery is connected across a \(5~\Omega\) resistor, it supplies a current of \(2~\text{A}\). The value of \(r\) is: 

1.	\(2~\Omega\)	2	\(1~\Omega\)
3.	\(0.5~\Omega\)	4.	zero

In the circuit shown in figure find the value of r(internal resistance of the cell) for which power transferred by the cell is maximum

1.  $4\mathrm{\Omega }$

2.  $12\mathrm{\Omega }$

3.  $16\mathrm{\Omega }$

4.  $8\mathrm{\Omega }$

In the circuit shown in the figure below, the current supplied by the battery is:
 
1. \(2~\text A\) 
2. \(1~\text A\) 
3. \(0.5~\text A\) 
4. \(0.4~\text A\) 

If a resistance coil is made by joining in parallel two resistances each of 20$\Omega$. An emf of 2V is applied across this coil for 100 seconds. The heat produced in the coil is

(1) 20 J

(2) 10 J

(3) 40 J

(4) 80 J

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

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.  $\frac{5}{3} \mathrm{A}$