Test on Electrostatic Potential and Capacitance

Two identical capacitors have the same capacitance C. One of them is charged to potential V₁ and the other to V₂. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

Three circular coils carrying currents I, 2I and 3I and having radius r, 2r and 3r respectively are arranged such that there centres coincide and their planes are mutually perpendicular. The magnitude of the magnetic field at the centre is

Two conducting rings A and B of radii r and 3r rolls uniformly in opposite directions with velocities of centres of mass 2V and V respectively on conducting surface s. There is a uniform magnetic field of magnitude B perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

A 10 volt battery has charged a capacitor of C = 20 μF fully. Then the amount of heat released in this process is

An uncharged parallel plate capacitor having a dielectric of constant K is connected to a similar air cored parallel capacitor charged to a potential V. The two share the charge and the common potential is V'. The dielectric constant K is