In the circuit shown in the figure, the total charge in \(750\, \mu C\) and the voltage across capacitor \(C _{2}\) is \(20\, V\). Then the charge on capacitor \(C _{2}\) is\(....\mu C\)

A \(220 \; V , 50 \; Hz\) AC source is connected to a \(25 \; V\), \(5 \; W\) lamp and an additional resistance \(R\) in series (as shown in figure) to run the lamp at its peak brightness, then the value of \(R\) (in ohm) will be

If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately ........ minutes (Take : \(g =10 \,ms ^{-2},\) the radius of earth, \(R =6400 \times 10^{3}\, m ,\) Take \(\left.\pi=3.14\right)\)

A spring whose unstretched length is \(\ell \) has a force constant \(k\). The spring is cut into two pieces of unstretched lengths \(\ell_1\) and \(\ell_2\) where, \(\ell_1 = n\ell_2\) and \(n\) is an integer. The ratio \(k_1/k_2\) of the corresponding force constants, \(k_1\) and \(k_2\) will be

A small ball of mass \(m\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_0\). After sometime, the ball falls with constant velocity. The viscous force on the ball is _______.

Two radioactive materials \(A\) and \(B\) have decay constants \(10\,\lambda \) and \(\lambda \), respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of \(B\) will be \(1/e\) after a time

The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \(\tau_{1}\) to \(\tau_{2} .\) If \(\frac{C_{p}}{C_{v}}=\gamma\) for this gas then a good estimate for \(\frac{\tau_{2}}{\tau_{1}}\) is given by :

In the given circuit, value of \(Y\) is

During the propagation of electromagnetic waves in a medium

An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) are connected in series with a \(220\,V\) ac source. If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x} A\). The value of \(x\) is -