A steady dc current of 100 A is flowing through a power module (S, D) as shown in Figure (a). The V-I characteristics of the IGBT (S) and the diode (D) are shown in Figures (b) and (c), respectively. The conduction power loss in the power module (S, D), in watts, is ________.

The switches $$T1$$ and $$T2$$ in Figure are switched in a complementary fashion with sinusoidal pulse width modulation technique. The modulating voltage $${v_m}\left( t \right) = 0.8\sin \left( {200\pi t} \right)\,\,V$$ and the triangular carrier $$\left( {{V_c}} \right),$$ voltage $$\left( {{V_c}} \right)$$ are as shown in figure $$(b).$$ The carrier frequency is $$5$$ $$kHz.$$ The peak value of the $$100$$ $$Hz$$ component of the load current $$\left( {{i_L}} \right)$$ in Ampere, is ______.

A buck converter, as shown in Figure $$(a)$$ below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure $$(b)$$ shows the inductor voltage $${V_L}$$ during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ________.

A single-phase transmission line has two conductors each of 10 mm radius. These are fixed at a center-to-center distance of 1 m in a horizontal plane. This is now converted to a three-phase transmission line by introducing a third conductor of the same radius. This conductor is fixed at an equal distance D from the two single-phase conductors. The three-phase line is fully transposed. The positive sequence inductance per phase of the three phase system is to be 5% more than that of the inductance per conductor of the single phase system. The distance D, in meters, is ________.