Different combination of \(3\) resistors of equal resistance \(R\) are shown in the figures.
The increasing order for power dissipation is:

A force of \(10 \; N\) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be ...... \(N\)

Due to presence of an em-wave whose electric component is given by \(\mathrm{E}=100 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}\), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where \(\lambda\) is the decay constant)

The total charge enclosed in an incremental volume of \(2 \times 10^{-9} \,{m}^{3}\) located at the origin is ...... \(nC,\) if electric flux density of its field is found as \(D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}\)

The force of interaction between two atoms is given by \(F\, = \,\alpha \beta \,\exp \,\left( { - \frac{{{x^2}}}{{\alpha kt}}} \right);\) where \(x\) is the distance, \(k\) is the Boltzmann constant and \(T\) is temperature and \(\alpha \) and \(\beta \) are two constants. The dimension of \(\beta \) is

An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.

Two soap bubbles coalesce to form a single bubble. If \(V\) is the subsequent change in volume of contained air and \(S\) change in total surface area, \(T\) is the surface tension and \(P\) atmospheric pressure, then which of the following relation is correct?

A longitudinal wave is represented by \(x =10 \sin 2 \pi\left( nt -\frac{ x }{\lambda}\right) \,cm\). The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

A circular conducting coil of radius \(1\, {m}\) is being heated by the change of magnetic field \(\vec {B}\) passing perpendicular to the plane in which the coil is laid. The resistance of the coil is \(2\, \mu\, \Omega\). The magnetic field is slowly switched off such that its magnitude changes in time as \(B=\frac{4}{\pi} \times 10^{-3}\, {T}\left(1-\frac{{t}}{100}\right)\) The energy dissipated by the coil before the magnetic field is switched off completely is \(E=.....\,{m} J.\)

The electric potential at the surface of an atomic nucleus \((Z=50)\) of radius \(9 \times 10^{-13} cm\) is \(\alpha \times 10^6 V\). What is the value of \(\alpha\)?
(Charge of proton \(1.6 \times 10^{-19} C\) )

A hollow spherical shell at outer radius \(R\) floats just submerged under the water surface. The inner radius of the shell is \(r\). If the specific gravity of the shell material is \(\frac{27}{8}\) \(w.r.t.\) water, the value of \(r\) is\(......R\)