The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure What is the value of current at \(t = 4\,s\) ? ............... \(\mu  A\)

In the given figure, there is a circuit of potentiometer of length \(A B=10 \,{m}\). The resistance per unit length is \(0.1 \,\Omega\) per \({cm}\). Across \({AB}\), a battery of emf \({E}\) and internal resistance ' \({r}^{\prime}\) is connected. The maximum value of emf measured by this potentiometer is : (In \(V\))

Four resistances of \(15\; \Omega, 12\; \Omega, 4 \;\Omega\) and \(10\; \Omega\) respectively in cyclic order to form Wheats tone's network. The resistance that is to be connected in parallel with the resistance of \(10\; \Omega\) to balance the network is .................. \(\Omega\)

An \(\alpha\) particle and a carbon \(12\) atom has same kinetic energy \(K\). The ratio of their de-Broglie wavelength \(\left(\lambda_{a}: \lambda_{C 12}\right)\) is

\(X\) different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number \({n}=6\) ? The value of \({X}\) is ..... .

An electron (mass \(m\)) with initial velocity \(\overrightarrow{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{i}}+\mathrm{v}_{0} \hat{\mathrm{j}}\) is in an electric field \(\overrightarrow{\mathrm{E}}=-\mathrm{E}_{0} \hat{\mathrm{k}} .\) If \(\lambda_{0}\) is initial de-Broglie wavelength of electron, its de-Broglie wave length at time \(t\) is given by

Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum)

A spring stretches by \(2\) mm when it is loaded with a mass of \(200\) g. From equilibrium position the mass is further pulled down by \(2\) mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g \(= 10\) m/s\(^2\))

The equation of state of a real gas is given by \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where \(\mathrm{P}, \mathrm{V}\) and \(\mathrm{T}\) are pressure. volume and temperature respectively and \(R\) is the universal gas constant. The dimensions of \(\frac{a}{b^2}\) is similar to that of :

A \(9\, V\) battery with internal resistance of \(0.5\,\Omega \) is connected across an infinite network as shown in the figure. All ammeters \(A_1 , A_2, A_3\) and voltmeter \(V\) are ideal. Choose correct statement