The integral

$$ \frac{1}{\pi} \int\limits_0^{\infty} \frac{x^{2026}}{\left(1+x^{2026}\right)\left(1+x^2\right)} d x $$

evaluates to $\_\_\_\_$

(Round off to two decimal places)

The figure shows a straight-line approximation for the forward characteristics of a power diode. A continuous on-state current of 15 A is flowing through the diode.

What is the power loss in the diode?

Consider the circuit shown in Figure (a). A gate pulse $v_g$ is applied between time instants $t_0$ and $t_1$. After $t_1$, during the MOSFET turn OFF process, it experiences a voltage overshoot.

Based on the $v_{d s}$ waveforms shown in Figure (b), which one of the following options is correct?

Consider the circuit shown. Assume that the diode $D$ is ideal. The supply voltage $v_s=325 \sin (2 \pi 50) \vee, L=500 \mu \mathrm{H}$, and $R=10 \Omega$. The peak diode current (in amperes) is $\_\_\_\_$ . (Round off to one decimal place)