A wire of resistance \(12~\Omega \text{m}^{-1}\) is bent to form a complete circle of radius \(10~\text{cm}\). The resistance between its two diametrically opposite points, \(A\) and \(B\) as shown in the figure, is:

                         
1. \(0.6\pi~\Omega\)
2. \(3~\Omega\)
3. \(6\pi~\Omega\)
4. \(6~\Omega\)

A student measures the terminal potential difference \((V)\) of a cell (of emf \(\varepsilon \)$$ and internal resistance \(r\)) as a function of the current \((I)\) flowing through it. The slope and intercept of the graph between \(V\) and \(I,\) then respectively, equal:
1. \(\varepsilon \) and \(-r\)
2. \(-r\) and \(\varepsilon \)
3.   \(r\) and \(-\varepsilon \)
4. \(-\varepsilon \) and \(r\)

A galvanometer having a coil resistance of $60\Omega$ shows full scale deflection when a current of 1.0A passes through it. It can be converted into an ammeter to read currents upto 5.0A by 

(a) putting in series resistance of 240$\Omega$

(b) putting in parallel resistance of 240$\Omega$

(c) putting in series resistance of 15$\Omega$

(d) putting in parallel resistance of 15$\Omega$

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$\Omega$

In the figure a long uniform potentiometer wire AB is having a constant potential gradient along its length. The null points for the two primary cells of emfs E₁ and E₂ connected in the manner shown are obtained at a distance of 120 cm and 300 cm from the end A. Find (i) $\frac{E_1}{E_2}$and  position of null point for the cell E₁.

How is the sensitivity of a potentiometer increased ?

Using Kirchoffs rules determine the value of unknown resistance R in the circuit so that no current flows through 4 Ω resistance. Also find the potential difference between A and D.