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 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.

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