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

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

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

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

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

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

$\mathrm{In} \mathrm{the} \mathrm{circuit} \mathrm{shown} \mathrm{in} \mathrm{figure} \mathrm{if} \mathrm{power} \mathrm{dissipated} \mathrm{in} 9\mathrm{\Omega } \mathrm{resistor} \mathrm{is} 144\mathrm{W}, \mathrm{then} \mathrm{potential} \mathrm{difference} \mathrm{across} 3.6\mathrm{\Omega } \mathrm{resistor} \mathrm{will} \mathrm{be}$

1.  36V

2.  18V

3.  9V

4.  Zero

The 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.  $\frac{5}{3}$ $\mathrm{A}$

A meter bridge is set up to determine unknown resistance x using a standard 10 $\Omega$ resistor. The galvanometer shows the null point when the tapping key is at a 52 cm mark. End corrections are 1 cm and 2 cm respectively for end A and B. Then the value of x is:

1.  10.2 $\Omega$

2.  10.6 $\Omega$

3.  10.8 $\Omega$

3. 11.1 $\Omega$

When a piece of aluminum wire of finite length is drawn through a series of dies to reduce its diameter to half its original value, its resistance will become :

(1) Two times

(2) Four times

(3) Eight times

(4) Sixteen times

Masses of 3 wires of same metal are in the ratio 1 : 2 : 3 and their lengths are in the ratio 3 : 2 : 1. The electrical resistances are in ratio

(1) 1 : 4 : 9

(2) 9 : 4 : 1

(3) 1 : 2 : 3

(4) 27 : 6 : 1

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

Express which of the following setups can be used to verify Ohm’s law 

(1)
(2)
(3)
(4)

The reading of the ammeter as per figure shown is

(1) $\frac{1}{8}A$

(2) $\frac{3}{4}A$

(3) $\frac{1}{2}A$

(4) 2 A