A potentiometer circuit is set up as shown.The potential gradient across the potentiometer wire, is k volt/cm and the ammeter, present in the circuit, reads 1.0A when two way key is switched off. The balance points, when the key between the terminals (i) 1 and 2 (ii) 1and 3, is plugged in, are found to be at lengths $l_{1}cm and l_{2}cm$ respectively.The magnitudes, of the resistors R and X, in ohm, are then, equal, respectively, to

(a)$k\left(l_2-l_1\right) and k{l}_2$

(b)$k{l}_1 and k\left(l_2-l_1\right)$

(c)$k\left(l_2-l_1\right)and k{l}_1$

(d)$k{l}_1 and k{l}_2$

 Consider the following two statements :

(1) Kirchhoff's junction law follows from the conservation of charge.

(2) Kirchhoff's loop law follows from the conservation of energy.

     Which of the following is correct?

(a) Both (A) and (B) are wrong

(b) (A) is correct and (B) is wrong

(3) (A)  is wrong and (B) is correct

(4) Both (A) and (B) are correct

                         
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 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

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

(a) 6.3 min

(b) 8.4 min

(c) 12.6 min

(d) 4.2 min

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

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.