A square loop of side $1 \mathrm{m}$ and resistance $1 \mathrm{\Omega }$ is placed in a magnetic field of $0.5 \mathrm{T}$. If the plane of loop is perpendicular to the direction of magnetic field, the magnetic flux through the loop is:

An inductor of inductance $L$, a capacitor of capacitance $C$ and a resistor of resistance $R$ are connected in series to an ac source of potential difference $V$ volt as shown in figure.Potential difference across $L,C$ and $R$ is $40 \mathrm{V},10 \mathrm{V}$ and $40 \mathrm{V}$, respectively. The amplitude of current flowing through $\text{L-C-R}$ series circuit is $10\sqrt{2} \mathrm{A}$. The impedance of the circuit is :

The magnetic flux linked with a coil (in $\mathrm{Wb}$) is given by the equation  $\varphi =5t^2+3t+16$. The magnitude of induced emf in the coil at the fourth second will be: