Two long parallel wires whose centres are at a distance $d$ apart carry equal currents in opposite directions. If the flux within the wires is neglected,the inductance of such an arrangement of wire of length $l$ and radius $a$ will be

$A$ coil having $N$ turns and resistance $R$ $\Omega$ is connected to a galvanometer of resistance $6R$ $\Omega$. The magnetic flux linked with this coil changes from $\phi_1$ weber to $\phi_2$ weber in time $t$ second. The induced current in the circuit is

The current $i$ in a coil varies with time as shown in the figure. The variation of induced $emf$ with time would be:

$A$ magnet is made to oscillate with a particular frequency,passing through a coil as shown in the figure. The time variation of the magnitude of $e.m.f.$ generated across the coil during one cycle is

$A$ semicircle conducting ring of radius $R$ is placed in the $xy$ plane,as shown in the figure. $A$ uniform magnetic field is set up along the $x$-axis. No $emf$ will be induced in the ring if:

When a coil is placed in a time-dependent magnetic field, the power dissipated in it is $P$. The number of turns, area of the coil, and radius of the coil wire are $N, A$, and $r$ respectively. For a second coil, the number of turns, area, and radius are $2N, 2A$, and $3r$ respectively. When the first coil is replaced with the second coil, the power dissipated in it is $\alpha P$. The value of $\alpha$ is . . . . . . .