What is the current through the battery in the circuit shown below?

In the given circuit of potentiometer, the potential difference \(E\) across \(AB\) ( \(10\, m\) length) is larger than \(E _{1}\) and \(E _{2}\) as well. For key \(K _{1}\) (closed), the jockey is adjusted to touch the wire at point \(J_{1}\) so that there is no deflection in the galvanometer. Now the first battery \(\left( E _{1}\right)\) is replaced by second battery \(\left( E _{2}\right)\) for working by making \(K _{1}\) open and \(K _{2}\) closed. The galvanometer gives then null deflection at \(J _{2}\). The value of \(\frac{ E _{1}}{ E _{2}}\) is \(\frac{ a }{ b },\) where \(a =\) ...............

A \(10\,\mu C\) charge is divided into two parts and placed at \(1\,cm\) distance so that the repulsive force between them is maximum. The charges of the two parts are :

A series \(LCR\) circuit is subjected to an AC signal of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\). If the voltage across the inductor \((\mathrm{L}=10 \mathrm{mH})\) is \(31.4 \mathrm{~V}\), then the current in this circuit is _______.

Statement \(I :\) The ferromagnetic property depends on temperature. At high temperature, ferromagnet becomes paramagnet. Statement \(II :\) At high temperature, the domain wall area of a ferromagnetic substance increases. In the light of the above statements, choose the most appropriate answer from the options given below :

Match the List\(-I\) with List\(-II\).

List \(I\)	List \(II\)
\(A\) \(AC\) generator	\(I\) Presence of both \(L\) and \(C\)
\(B\) Transformer	\(II\) Electromagnetic Induction
\(C\)Resonance phenomenon to occur	\(III\) Quality factor
\(D\)Sharpness of resonance	\(IV\) Mutual Inductance

Choose the correct answer from the options given below:

A particle which is experiencing a force, given by \(\vec F = 3\vec i -12\vec j\), undergoes a displacement of \(\vec d = 4\vec i\) . If the particle had a kinetic energy of \(3\, J\) at the beginning of the displacement, what is its kinetic energy at the end of the displacement?

An electric bulb rated as \(200\, {W}\) at \(100 \,{V}\) is used in a circuit having \(200\, {V}\) supply. The resistance \('R'\) that must be put in series with the bulb so that the bulb delivers the same power is \(.....\,\Omega\)

Two gases-argon (atomic radius \(0.07 \;\mathrm{nm}\),atomic weight \(40\) ) and xenon (atomic radius \(0.1\; \mathrm{nm},\) atomic weight \(140\) ) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears \(2\; beats/sec\). The oscillation frequency of each tuning fork is \(v_{0}=1400 \;\mathrm{Hz}\) and the velocity of sound in air is \(350\; \mathrm{m} / \mathrm{s}\). The speed of each tuning fork is close to