The magnetic field in a region is given by $\overrightarrow{B}=B_0\left|1+\frac{x}{a}\right| \hat{k}$ A square loop of edge - length $d$ is placed with its edge along $x\hspace{0.17em}\& y$ axis. The loop is moved with constant velocity $\overrightarrow{v}=v_0\hat{i}$. The emf induced in the loop is

A triangular wire frame (each side $=2 \mathrm{m}$) is placed in a region of time variant magnetic field $\frac{dB}{dt}=\sqrt{3} \mathrm{T} {\mathrm{s}}^{-1}$. The magnetic field is perpendicular to the plane of the triangle and its centre coincides with the centre of triangle. The base of the triangle $AB$ has a resistance $1\Omega$ while the other two sides have resistance $2\Omega$ each. The magnitude of potential difference between the points $A$ and $B$ will be

The ratio of time constant in charging and discharging in the circuit shown in figure is

For $L-R$ circuit, the time constant is equal to

A circuit element is placed in a closed box. At time $t=0,$ a constant current generator supplying a current of $1 A$ is connected across the box. Potential difference across the box varies according to graph shown in the figure. The element in the box is

Current growth in two $L-R$ circuits $\left(B\right)$ and $\left(C\right)$ as shown in figure $\left(A\right)$. Let $L_1,L_2,R_1$ and $R_2$ be the corresponding values in two circuits. Then