The resistances in the two gaps of a balanced meter bridge are 'X' $\Omega$ and '3X' $\Omega$ respectively. If the resistances are interchanged the balance point shifts by

A current carrying circular coil of radius 'R' produces magnetic field $B_1$ at an axial point P at a distance 'x' from its centre and $B_2$ at point Q placed at its centre respectively . If $B_2 = 8B_1$, the value of x is

The magnetic induction produced inside an ideal solenoid, depends on which of the following quantities ?
(a) number of turns per unit length.
(b) radius of the wire.
(c) current flowing throught it.
(d) permeability of the medium.

Two coils P and S have a mutual inductance of ($\pi$) mH. The secondary coil S has resistance $4\,\Omega$ and self inductance $(60/\pi)$ mH. If the current in the primary is $I_p = 12\sin(50\pi t)$, then the maximum value of the current induced in coil S is [Take $\pi^2 = 10$]