Consider the boost converter circuit shown. Assume that the semiconductor devices are ideal. In steady state, the inductor current rises linearly from 0 A to 6 A in the first $10 \mu \mathrm{~s}$ and then falls linearly from 6 A to 0 A in the next $10 \mu \mathrm{~s}$ of every switching cycle as shown. The load resistance R is $10 \Omega$ and the capacitance C is $50010 \mu \mathrm{~F}$.

Neglect the ripple in the output voltage. What is the input voltage $V_{d c}$ ?

In the DC-DC converter shown in the figure, the current through the inductor is continuous. The switching frequency is 500 Hz. The voltage ($V_o$) across the load is assumed to be constant and ripple free. The peak inductor current in amperes is __________ (rounded off to the nearest integer).

The circuit shown in the figure has reached steady state with thyristor 'T' in OFF condition. Assume that the latching and holding currents of the thyristor are zero. The thyristor is turned ON at $$t=0$$ sec. The duration in microseconds for which the thyristor would conduct, before it turns off, is _________ (Round off to 2 decimal places).