The magnetic moments associated with two closely wound circular coils a and b of radius $r$ and $2r$ respectively are equal if (where $N_a$, $I_a$ and $N_b$, $I_b$ are number of turns and current in A and B respectively)

A conducting loop of radius $10/[\pi]^{1/2}$ cm is placed perpendicular to a uniform magnetic field $0.5$ T. The magnetic field is decreased to zero in $0.5$ s at a steady rate. The induced emf in the circular loop at $0.25$ s is

In the circuit shown, the ratio of the quality factor and the band width is
(Given: band width = R/L)

An inductor of $0.5$ mH, a capacitor of $20$ $\mu$F and resistance $20\,\Omega$ are connected in series with a $220$ V ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2}$ A. The value of $x$ is