In the given circuit, the voltage across load resistance \(\left(R_L\right)\) is _______.

An alternating \(emf\) \(E =440 \sin 100 \pi t\) is applited to a circuit containing an inductance of \(\frac{\sqrt{2}}{\pi} H\). If an a.c. ammeter is connected in the circuit, its reading will be \(.......A\)

An object is at a distance of \(20\,m\) from a convex lens of focal length \(0.3\,m.\) The lens forms an image of the object. If the object moves away from the lens at a speed of \(5\,m/s,\) the speed and direction of the image will be

Two capacitors, each having capacitance \(40\,\mu F\) are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant \(K\) such that the equivalence capacitance of the system became \(24\,\mu F\). The value of \(K\) will be.

A block moving horizontally on a smooth surface with a speed of \(40\, {m} / {s}\) splits into two parts with masses in the ratio of \(1: 2\). If the smaller part moves at \(60\, {m} / {s}\) in the same direction, then the fractional change in kinetic energy is :-

In the given circuit, \(C _1=2\,\mu F , C _2=0.2\,\mu F\), \(C _3=2\,\mu F , C _4=4\,\mu F,\) \(C _5=2\,\mu F , C _6=2\,\mu F\), the charge stored on capacitor \(C _4\) is \(.....\mu C\).

If the charge on a capacitor is increased by \(2C\), the energy stored in it increases by \(44 \%\). The original charge on the capacitor is (in \(C\) )

A circular disc reaches from top to bottom of an inclined plane of length \('L'.\) When it slips down the plane, it takes time \('t_{1}'\). when it rolls down the plane, it takes time \(t_{2}\). The value of \(\frac{t_{2}}{t_{1}}\) is \(\sqrt{\frac{3}{x}}\). The value of \(x\) will be .... .

If \(B\) is magnetic field and \(\mu_0\) is permeability of free space, then the dimensions of \(\left(B / \mu_0\right)\) is

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

A passenger train of length \(60\, m\) travels at a speed of \(80\, km/hr\). Another freight train of length \(120\, m\) travels at a speed of \(30\, km/hr\). The ratio of times taken by the passenger train to completely cross the freight train when: \((i)\) they are moving in the same direction, and \((ii)\) in the opposite directions is