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

1. ${\epsilon }_1-\left(i_1+i_2\right)R-i_1{r}_1=0$

2. ${\epsilon }_2-i_2{r}_2-{\epsilon }_1-i_1{r}_1=0$

3. $-{\epsilon }_2-\left(i_1+i_2\right)R+i_2{r}_2=0$

4. ${\epsilon }_1-\left(i_1+i_2\right)R+i_1{r}_1=0$

A current of 3A flows through the 2$\Omega$ resistor shown in the circuit. The power dissipated in the $5\Omega$ resistor is

(a) 4 W                                              (b) 2 W

(c) 1 W                                              (d) 5 W

A wire of a certain material is streched slowly by ten per cent. Its new resistance and specific resistance become respectively 

(1) 1.2 times, 1.1 times

(2) 1.21 times,same 

(3) both remain the same

(4) 1.1 times, 1.1 times

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

(1) 1.0 $\Omega$

(2) 0.5 $\Omega$

(3) 2.0 $\Omega$

(4) zero 

In the circuit shown, the current through the 4 $\Omega$ resistor is 1 A when the points P and M are connected to a DC voltage source. The potential difference  between the points M and N is 

1. 1.5 V 

2. 1.0 V

3. 0.5 V 

4. 3.2 V

A galvanometer of resistance 50$\Omega$ is connected to a battery of 3 V along with a resistance of 2950 $\Omega$ in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 20 divisions, the resistance in series should be 

(a) 5050$\Omega$

(b) 5550 $\Omega$

(c) 6050 $\Omega$

(d) 4450$\Omega$

A capacitor of capacitance 5 μF is connected as shown in the figure. The internal resistance of the cell is 0.5 Ω. The amount of charge on the capacitor plate is?

(1) 0 μC

(2) 5 μC

(3) 10 μC

(4) 25 μC

In the circuit here, the steady state voltage across capacitor C is a fraction of the battery e.m.f. The fraction is decided by 

(1) R₁ only

(2) R₁ and R₂ only

(3) R₁ and R₃ only

(4) R₁, R₂ and R₃

In the figure below, what is the potential difference between the point A and B and between B and C respectively in steady state 

(1) $V_{AB}=V_{BC}=100V$

(2) $V_{AB}=75V,V_{BC}=25V$

(3) $V_{AB}=25V,V_{BC}=75V$

(4) $V_{AB}=V_{BC}=50V$

In the given figure each plate of capacitance C has partial value of charge equal to:

1. CE

2. $\frac{CE{R}_1}{R_2-r}$

3. $\frac{CE{R}_2}{R_2+r}$

4. $\frac{CE{R}_1}{R_1-r}$