A 10 cm long perfectly conducting wire PQ is moving with a velocity I cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1$$\Omega $$ as shown in figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is x $$ \times $$ 10^-3 A, where the value of x is ...........

[Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given e^-1 = 0.37, where e is base of the natural logarithm]

Two inductors L₁ (inductance 1mH, internal resistance 3$$\Omega$$) and L₂ (inductance 2 mH, internal resistance 4$$\Omega$$), and a resistor R (resistance 12$$\Omega$$) are all connected in parallel across a 5V battery. The circuit is switched on at time t = 0. The ratio of the maximum to the minimum current (I_max / I_min) drawn from the battery is

A circular wire loop of radius R is placed in the xy plane centred at the origin O. A square loop of side a(a << R) having two turns is placed with its centre at z = $$\sqrt3$$R along the axis of the circular wire loop, as shown in the figure. The plane of the square loop makes an angle of 45$$^\circ$$ with respect to z-axis. If the mutual inductance between the loops is given by $${{{\mu _0}{a^2}} \over {{2^{p/2}}R}}$$, then the value of p is ___________.