A capacitor is connected to a \(20\, {V}\) battery through a resistance of \(10\, \Omega .\) It is found that the potential difference across the capacitor rises to \(2\, {V}\) in \(1\, \mu {s}\). The capacitance of the capacitor is \(....\,\mu {F}\) Given : \(\ln \left(\frac{10}{9}\right)=0.105\)

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of \(2 \,\Omega\). The value of internal resistance of each cell is ............ \(\Omega\)

Two identical electric point dipoles have dipole moments \(\overrightarrow{p}_{1}= p\hat i\) and \(\overrightarrow{p}_{2}=- p\hat i\) and are held on the \(x-\)axis at distance \('a'\) from each other. When released, they move along the \(x-\)axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is \('m',\) their speed when they arc infinitely far apart is

A long straight wire of circular cross-section (radius \(a\)) is carrying steady current \(I\). The current \(I\) is uniformly distributed across this cross-section. The magnetic field is

Two wires \(A\) and \(B\) are made up of the same material and have the same mass. Wire A has radius of \(2.0 \mathrm{~mm}\) and wire \(B\) has radius of \(4.0 \mathrm{~mm}\). The resistance of wire B is \(2 \Omega\). The resistance of wire \(\mathrm{A}\) is _______ \(\Omega\).

Given below are two statements: Statement\(- I\) : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement\(- II\): Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the \(CORRECT\) answer from the options given below : -

In the following \(p-V\) diagram the equation of state along the curved path is given by \((V-2)^2=4\) ap where \(a\) is a constant. The total work done in the closed path is

A monochromatic source of light operating at \(15\) kW emits \(2.5\times 10^{22}\) photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take \(h=6.6\times 10^{-34}\) J·s and \(c=3\times 10^8\) m/s).

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is \(915\)\(A\). The longest wavelength of spectral lines in the Balmer series will be _______ \(A\).

In a hydrogen atom the electron makes a transition from \(( n +1)^{\text {th }}\) level to the \(n ^{\text {th }}\) level. If \(n>>1,\) the frequency of radiation emitted is proportional to

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance \(2000 \,\Omega\) is used to measure the potential difference across \(500 \,\Omega\) resister, the reading of the voltmeter will be ............... \(V\)

The speed of a longitudinal wave in a metallic bar is \(400~m/s.\) If the density and Young's modulus of the bar material are increased by 0.5% and 1% respectively then the speed of the wave is changed approximately to ___________ \(m / s\).