A part of a complete circuit is shown in the figure. At some instant, the value of current \(I\) is \(1\, A\) and it is decreasing at a rate of \(10^{2}\, A s ^{-1}\) The value of the potential difference \(V _{ P }- V _{ Q }\) (in volts) at that instant, is.

Given below are two statements: Statement \(I:\) If \(E\) be the total energy of a satellite moving around the earth, then its potential energy will be \(\frac{E}{2}\). Statement \(II:\) The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \(E\). In the light of the above statements, choose the most appropriate answer from the options given below

The displacement of a particle, executing simple harmonic motion with time period \(T\), is expressed as \(x(t)= A \sin \omega t\), where \(A\) is the amplitude. The maximum value of potential energy of this oscillator is found at \(t=T / 2 \beta\). The value of \(\beta\) is ___________.

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is

The specific heat at constant pressure of a real gas obeying \(\mathrm{PV}^2=\mathrm{RT}\) equation is _______.

A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \(x \times 10^{15}\,Hz\). The value of \(x\) is (Given \(h =4.25 \times 10^{-15}\,eVs\) )

The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:-

If two charges \(q _1\) and \(q _2\) are separated with distance ' \(d\) ' and placed in a medium of dielectric constant \(K\). What will be the equivalent distance between charges in air for the same electrostatic force?

Two resistors \(2 \Omega\) and \(3 \Omega\) are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY . When an unknown resistor is connected in parallel with \(3 \Omega\) resistor, the null point is shifted by 22.5 cm toward Y . The resistance of unknown resistor is _________ \(\Omega\).