An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ___________. \((\pi=3.14)\)

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A :\) Photodiodes are preferably operated in reverse bias condition for light intensity measurement. Reason \(R\) : The current in the forward bias is more than the current in the reverse bias for a \(p - n\) junction diode. In the light of the above statement, choose the correct answer from the options given below :

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is \({\theta _{iC}}\) and Brewster's angle of incidence is \({\theta _{iB}}\), such that \(\sin \,{\theta _{iC}}/\sin \,{\theta _{iB}} = \eta  = 1.28\). The  relative refractive index of the two media is

In a Frank-hertz experiment, an electron of energy \(5.6\,eV\) passes through mercury vapour and emerges with an energy \(0.7\,eV.\) The minimum wavelength of photons emitted by mercury atoms is close to ............. \(nm\)

To find the focal length of a convex mirror, a student records the following data

Object Pin	Convex Lens	Convex Mirror	Image Pin
\(22.2\,cm\)	\(32.2\,cm\)	\(45.8\,cm\)	\(71.2\,cm\)

The focal length of the convex lens is \(f_1\)  and that of mirror is \(f_2\). Then taking index correction to be negligibly small, \(f_1\)  and  \(f_2\) are close to

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda _1/\lambda _2\), of the photons emitted in this process is

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm.

Two cells of emf 1 V and 2 V and internal resistance \(2 \Omega\) and \(1 \Omega\), respectively, are connected in series with an external resistance of \(6 \Omega\). The total current in the circuit is \(\mathrm{I}_1\). Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is \(I_2\). The value of \(\left(\frac{I_1}{I_2}\right)\) is \(\frac{x}{3}\). The value of \(x\) is _____.

A glass tumbler having inner depth of \(17.5\, {cm}\) is kept on a table. A student starts pouring water \((\mu=4 / 3)\) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (In \(cm\))

As per the given graph choose the correct representation for curve \(A\) and curve \(B\).Where \(X _{ C }=\) reactance of pure capacitive circuit connected with \(A.C.\) source \(X _{ L }=\) reactance of pure inductive circuit connected with \(A.C.\) source \(R =\) impedance of pure resistive circuit connected with \(A.C.\) source \(Z =\) Impedance of the LCR series circuit \(\}\)

A galvanometer, whose resistance is \(50\,ohm,\) has \(25\) divisions in it. When a current of \(4\times 10^{-4}\,A\) passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of range \(2.5\,V,\) it should be connected to a resistance of.......\(ohm\)