A bulb and a capacitor are connected in series across an AC supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

12 wires each having resistance \(2 \Omega\) are joined to form a cube. A battery of \(6 \mathrm{~V}\) emf is joined across point \(\mathrm{a}\) and \(\mathrm{c}\). The voltage difference between \(e\) and \(f\) is ______V.

Two thermodynamical process are shown in the figure. The molar heat capacity for process \(A\) and \(B\) are \(C_A\) and \(C_B\). The molar heat capacity at constant pressure and constant volume are represented by \(C_P\) and \(C_V\), respectively. Choose the correct statement.

A bead of mass ' \(m\) ' slides without friction on the wall of a vertical circular hoop of radius ' \(R\) ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' \(R\) '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity)

The pressure and volume of an ideal gas are related as \(\mathrm{PV}^{3 / 2}=\mathrm{K}\) (Constant). The work done when the gas is taken from state \(A\left(P_1, V_1, T_1\right)\) to state \(\mathrm{B}\left(\mathrm{P}_2, \mathrm{~V}_2, \mathrm{~T}_2\right)\) is _______.

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by

When the \(rms\) voltages \(V_L, V_C\) and \(V_R\) are measured respectively across the inductor \(L\), the capacitor \(C\) and the resistor \(R\) in a series \(LCR\) circuit connected to an \(AC\) source, it is found that the ratio \(V_L : V_C : V_R = 1 : 2 : 3\). If the \(rms\) voltage of the \(AC\) sources is \(100\, V\), the \(V_R\) is close to........\(V\)

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is \(5.0 \mathrm{~cm}\). The magnitude of the magnetic field at a point \(P\) midway between the wires is __________\(\mu \mathrm{T}\) (Given : \(\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\) )

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is \(....\,{mm} .\) [Refractive index of air \(=1.0003\), wavelength of yellow light in vacuum \(=6000 \,\mathring {{A}}\) ]

For a charged spherical ball, electrostatic potential inside the ball varies with \(r\) as \(V =2 ar ^2+ b\). Here, \(a\) and \(b\) are constant and \(r\) is the distance from the center. The volume charge density inside the ball is \(-\lambda a \varepsilon\). The value of \(\lambda\) is \(...........\). \(\varepsilon=\) permittivity of medium.

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) )

A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same plane as the bar. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency \( \omega \). The ratio of v and \( \omega \) is: